Philanthropist Tom Steyer stands in front of one of the billboards he has funded in Times Square calling for the impeachment of President Donald Trump on November 20, 2017 in New York City. Getty Images

Billionaire Tom Steyer is leading a multimillion-dollar effort to remove Donald Trump from the presidency. He is also looking into pursuing the job himself — especially if Democrats do well in elections this fall. Steyer has said publicly that he's not ruling out a 2020 run for president. But behind the scenes, the former hedge-fund chief is taking a more aggressive approach toward launching a campaign for the White House, sources told CNBC. According to interviews with six people close to Steyer, the Democratic megadonor has privately indicated he's preparing to make a decision about running. He will likely run, these people added, if Democrats flip the House and make inroads in the Senate, where the GOP holds a razor-thin majority. Pundits give Democrats good odds to win the House, but Republicans are considered likely to keep control of the Senate.

"There's no secret he's going to be running for president, especially if Democrats take the House," a top Democratic donor told CNBC on the condition of anonymity. "Anyone who says this movement of his is purely about saving the country from Trump and not about any future political ambitions is just out of touch." Steyer associates also point to the work being done by Allen Nesbitt, the leader of opposition research firm Nesbitt Research, for Steyer's Need to Impeach super PAC, or NTI. They perceive it as another sign that the California billionaire is seriously exploring a run for president.

Research for Steyer

Steyer hired Nesbitt and his team in October 2017 to take the lead on research for NTI, as well as run its rapid response operations. "They're constantly looking at how issues that Tom works on resonate with voters — whether it be immigration, climate change, impeachment, or health care," Aleigha Cavalier, a spokeswoman for Steyer, said in an email. Steyer is also active in environmental issues. The firm's research inquiries aren't limited to gauging where voters stand on core issues for the 2018 midterms, according to a person familiar with Nesbitt's work with Steyer. They also appear to be measuring whether the electorate would support him for president if he ran on a platform featuring those issues. Steyer aides would not dispute that their boss is considering running for higher office but pushed back on the idea that Nesbitt's research is related to a 2020 run.

At the end of this election cycle, Tom plans to look at the best way he can make an impact moving forward, and all options are on the table. Kevin Mack lead strategist, Need to Impeach

"At the end of this election cycle, Tom plans to look at the best way he can make an impact moving forward, and all options are on the table," NTI lead strategist Kevin Mack said after CNBC asked whether Steyer is considering a run for the White House. Mack compared Nesbitt's work for Steyer to research conducted by other groups, such as Planned Parenthood. He argued that the efforts of Nesbitt's firm aren't necessarily linked to Steyer's 2020 ambitions. Nesbitt "has been doing research on any number of different things. Look at what the president has done at the border. Do we do a poll on that? Yes. Do we have research on that? Yes. Can the research be used for other purposes? I guess the answer is yes, possibly," Mack said. "But I guess I'm saying if Planned Parenthood runs a poll about women's rights, does that mean Cecile Richards is running for president? Not necessarily." Nesbitt himself declined to comment when reached by phone Thursday.

Loving the spotlight

From the outset of his campaign to remove Trump from office, friends and supporters have noticed how much Steyer enjoys the notoriety and name recognition he's gained from the onslaught of attacks he's laid upon the White House, according to two people with knowledge of the matter. With voters growing more aware of Steyer, his allies believe that his efforts to visit different parts of the country could give him the confidence he needs to take on a growing pool of potential Democratic presidential candidates. Former Vice President Joe Biden, Sen. Elizabeth Warren, D-Mass., Sen. Bernie Sanders, I-Vt., and Sen. Kamala Harris, D-Calif., are often mentioned as possible candidates.

"I think he's enjoying his notoriety and the celebrity piece to all of this," said a friend of Steyer's. "He loves going on TV, going in front of all these groups and people applauding. Don't forget one final piece of the puzzle: He's been right more than not. He's been right about Trump, energy issues and health care, and those are things to consider as well." Steyer just wrapped up a 30-stop town hall series where he urged attendees to vote this year — and sign his petition that requests Congress remove Trump from office. Last week Steyer stopped at the Iowa State Fair with a bunch of other possible Democratic nominees for president. At the event he said he has not ruled out jumping into the 2020 election and is waiting to see what happens in the midterms to make a decision. He did not elaborate further. When asked for Steyer's comment on this story, his representatives referred CNBC to his recent comments on the matter.

Cohen, Manafort fuel new Steyer push

Steyer's suggestion that he's thinking about running for office also comes as legal peril continues to grow around Trump. The president's former campaign boss, Paul Manafort, was found guilty of eight counts of federal financial crimes Tuesday, the same day Trump's former personal lawyer, Michael Cohen, pleaded guilty to eight federal charges. Cohen implicated Trump in a criminal scheme to commit campaign finance violations. Cohen's confession added some juice to Steyer's argument for impeachment. Need to Impeach immediately kicked off a $1 million national ad buy that will call for Trump's removal from office. It's not yet clear whether the topic of impeachment will resonate with voters as the midterms approach. House Minority Leader Nancy Pelosi, D-Calif., has called impeachment a "divisive issue," saying it's a message that should not be used by her party on the campaign trail. Polls show that voters are mixed about impeaching Trump, but that could change. A recent CNN poll showed that 42 percent of Americans support the idea of pushing Trump out of office. The poll was taken in June, two months before the Cohen and Manafort bombshells.

WATCH: Trump responds to Steyer's impeachment campaign