(CNN) When Marco Rubio dropped out of the GOP race, he made this clear: "I'll be a private citizen in January."

But that doesn't mean he's done with politics.

In private conversations with supporters and donors over the last several weeks, the 44-year-old Rubio repeatedly gets this advice: Run again, potentially in 2020, according to several people familiar with the conversations.

And Rubio, sources said, is certainly open to it. Some of his allies are even urging Rubio to withhold supporting Ted Cruz because such endorsements have made little difference this campaign season and the two could face off again in a future contest.

Despite his presidential stumbles this year, Rubio plans to be visible during the campaign season for House and Senate candidates, sources said. In particular, Rubio hopes to become a high-profile surrogate for many down-ballot Republicans who may decide to run away from their party's nominee if it's either Cruz or Donald Trump, the sources said.

Rubio allies said that doing so could help him rebuild his own brand and reconnect with GOP voters after being driven out of the race by Trump's dominance and failing to carry his home state of Florida.

Photos: Moments from Marco Rubio's career Photos: Moments from Marco Rubio's career Florida Sen. Marco Rubio speaks in October 2013 at the Values Voter Summit, held by the Family Research Council in Washington. Hide Caption 1 of 20 Photos: Moments from Marco Rubio's career Sen. Mike Lee, left, and Rubio talk before a news conference to introduce their proposal for an overhaul of the tax code in March. Hide Caption 2 of 20 Photos: Moments from Marco Rubio's career Rubio, center, arrives in the House chamber ahead of Israeli Prime Minister Benjamin Netanyahu's address to a joint meeting of the U.S. Congress in March. Hide Caption 3 of 20 Photos: Moments from Marco Rubio's career Rubio speaks with the media after delivering remarks during the graduation of small business owners from the Goldman Sachs 10,000 Small Businesses program held in Miami in February. Hide Caption 4 of 20 Photos: Moments from Marco Rubio's career Rubio talks to aides in December before speaking on President Barack Obama's announcement about revising policies on U.S.-Cuba relations. Hide Caption 5 of 20 Photos: Moments from Marco Rubio's career Rubio, left, talks to Sen. Lindsey Graham prior to a news conference on Capitol Hill in July. Hide Caption 6 of 20 Photos: Moments from Marco Rubio's career Rubio talks to reporters in June after a closed door briefing on Capitol Hill. Hide Caption 7 of 20 Photos: Moments from Marco Rubio's career Rubio speaks to the media in front of a wall dedicated to the victims of the violence in Venezuela as he shows support for the Venezuelan community at a restaurant in Doral, Florida, in April 2014. Hide Caption 8 of 20 Photos: Moments from Marco Rubio's career Rubio speaks to the media at the Doral restaurant in April 2014. Hide Caption 9 of 20 Photos: Moments from Marco Rubio's career Rubio checks his phone in March as he arrives for a Capitol Hill news conference to introduce a proposal for an overhaul of the tax code. Hide Caption 10 of 20 Photos: Moments from Marco Rubio's career Rubio, left, is greeted as he arrives at a restaurant in Doral in February 2014. Hide Caption 11 of 20 Photos: Moments from Marco Rubio's career Rubio, left, and Florida Gov. Rick Scott speak to the media in Doral in February 2014. Hide Caption 12 of 20 Photos: Moments from Marco Rubio's career From left, Sens. Cory Booker, Rubio, Kristen Gillibrand and John McCain wait for Obama to deliver the State of the Union address in January 2014. Hide Caption 13 of 20 Photos: Moments from Marco Rubio's career Rubio addresses an event held by the American Enterprise Institute for Public Policy Research in January 2014. Hide Caption 14 of 20 Photos: Moments from Marco Rubio's career Paralympian Brad Snyder poses with Rubio during a Team USA Congressional visit in November 2013. Hide Caption 15 of 20 Photos: Moments from Marco Rubio's career Rubio speaks in November 2013 during a campaign stop for Virginia Attorney General Ken Cuccinelli, the Republican candidate for governor of Virginia. Hide Caption 16 of 20 Photos: Moments from Marco Rubio's career Rubio confers with McCain as U.S. Ambassador to Syria Robert Ford testifies before the Senate Foreign Relations Committee in October 2013. Hide Caption 17 of 20 Photos: Moments from Marco Rubio's career Rubio, center, speaks to members of the media as Sen. Ron Johnson, left, and Rep. Ron DeSantis listen during a news conference on Capitol Hill in October 2013. Hide Caption 18 of 20 Photos: Moments from Marco Rubio's career Rubio returns to the Capitol after meeting with Obama and other Republican leaders about the government shutdown in October 2013. Hide Caption 19 of 20 Photos: Moments from Marco Rubio's career Rubio speaks to an aide on Capitol Hill as he arrives for the weekly Senate Republican Policy Committee luncheon in September 2013. Hide Caption 20 of 20

"In my opinion, he's not damaged from the campaign at all," said Wayne Berman, a major Rubio donor who declined to reveal his own private discussions with the senator. "I think everything that has happened in the campaign and since has enhanced his currency as a future candidate for public office."

One of Rubio's first tasks: Helping elect his close friend, Florida Lt. Gov. Carlos Lopez-Cantera, who is battling in a heavily contested GOP primary to fill the Senate seat that the freshman senator is vacating. Rubio plans to formally endorse Lopez-Cantera and campaign with the lieutenant governor within the next several weeks, sources said.

In an interview, Lopez-Cantera would only say the two have discussed the race and "there may be some news coming up in the next 30-60 days."

"I think he wants to ensure good Republicans get elected to office in Congress and the Senate," said Lopez-Cantera, a friend of Rubio's dating back to 1996 when the two worked together on Bob Dole's presidential campaign. "The actions you will see out of him will reflect that."

The low-turnout August primary could hinge on populous Miami-Dade County -- Rubio's home and an area where the Florida senator could help attract supporters for Lopez-Cantera.

"He's still very popular in the state," Lopez-Cantera said of Rubio.

Rubio's low profile -- for now

What remains to be seen is how much lasting damage the senator's failed presidential campaign has done to his image. While he lasted until March 15, he only won one state -- Minnesota -- as well as Puerto Rico and the District of Columbia. And his message -- often delivered with soaring oratory -- failed to connect with voters who were angry at the direction of Washington. His handling of Trump backfired dramatically, and there was ample second-guessing about his campaign strategy.

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After 2016, Rubio will leave the Senate after concluding one term in office and having accomplished very little legislatively. The one legislative issue he's most identified with -- immigration -- became a liability for him on the campaign trail after he abandoned his plan, which was reviled by right.

Yet in an era of simmering frustration with Washington, many Rubio allies believe that a long resume as a politician is actually a liability more than anything else. And they privately believe Rubio can remain relevant in the national debate even after leaving office.

Speaking to reporters on Capitol Hill soon after quitting the race last month, Rubio ruled out a future run for governor in Florida and said he would not be anyone's running mate in 2016. But he refused to discuss a possible 2020 run if the GOP does not win the White House in the fall.

When asked about his future political plans, Rubio said: "Guys, I just got here. ... I'm not running for governor, I'm not running for reelection to the Senate. Beyond that, I'm not" commenting.

Alex Burgos, a spokesman for Rubio, declined to discuss anything about the senator's plans.

"Sen. Rubio's primary focus is his work on behalf of the people of Florida in the United States Senate," Burgos said. "Next January, he will be a private citizen, and he has not been involved in any discussions about any future political races."

Some detractors liken the senator to Rick Perry, comparing Rubio's debate gaffe in New Hampshire -- where he repeated the same line despite coming under vigorous assault from New Jersey Gov. Chris Christie -- to the former Texas governor's debate stumbles in 2012. Perry waged a short-lived presidential campaign in 2016, and some expect Rubio to fair the same if he tries again in 2020.

But Rubio allies are arguing that many former GOP nominees have failed once only to succeed in their next campaigns.

Sen. Steve Daines, R-Montana, an early Rubio supporter, said the senator should try again.

"If there's ever been a time for someone to unite and inspire this country, it's now," Daines said Monday. "And I think Marco has that ability."

Cruz endorsement?

Rubio has told state party chairmen that he wants to hold onto his 173 delegates for now, an effort aimed at hurting Trump and potentially helping Cruz. Moreover, Rubio has asked for his name to be removed from the ballot in states that have yet to hold primary contests to ensure he does not siphon away any of the anti-Trump vote.

In his final days on the campaign trail, Rubio vowed to do everything possible to stop Trump, including driving around the country in his "pickup truck."

Yet, whether Rubio publicly gets behind Cruz -- the man best positioned to stop Trump -- remains to be seen. Some Rubio allies argue there's little value for him to throw his support behind his fellow senator. The reason: Rubio would have to walk back a number of his sharply barbed attacks at Cruz, including when Rubio called Cruz a "liar" and for running what he said was a dirty campaign. And stumping with Cruz would only give the Texas Republican fodder to use against Rubio if they were to face off again in 2020.

Moreover, one ally of Rubio's said privately that many donors dislike Cruz, so the Florida senator would hurt his own credibility by backing his former rival.

But perhaps the biggest reason to stay away: Trump is still the favorite to win the nomination and backing Cruz could do little to move the dial.

Berman, the former Rubio donor and the senator's former national finance chairman, said he had no opinion on whether Rubio should back Cruz.

But he added: "So far, endorsements have proven to be of somewhat limited impact."