Texas Congressman Beto O'Rourke gives his concession speech during on election night at Southwest University Park in downtown El Paso on November 6, 2018.

Since O'Rourke's loss earlier this month, Rob Friedlander , a senior advisor to the Texas Democrat's campaign, has received calls from the New Hampshire Young Democrats requesting that O'Rourke come to the Granite State, according to people familiar with the matter. The goal would be to have O'Rourke tour parts of the state and interact with voters.

Rep. Beto O'Rourke, who became a hero within the Democratic Party while losing a surprisingly tight race against Texas GOP Sen. Ted Cruz, has already been invited to New Hampshire to speak with voters and meet experienced political operators in the key primary state, CNBC has learned.

The New Hampshire Young Democrats "extended an invitation via email. No further action has been taken at this time," Chris Evans, a spokesman for the O'Rourke campaign confirmed to CNBC. Friedlander "was put on the email as the individual knew him from New Hampshire days, but Rob is not involved in working to set anything up," he added.

The group is a chapter of the Young Democrats of America, the official youth arm of the Democratic Party. According to NHYD's website, its mission is to "help young Democrats seeking office, advocate for progressive issues, and train the next generation of progressive leaders." O'Rourke was lauded during the campaign for galvanizing young voters.

Friedlander, meanwhile, was a New Hampshire field organizer for the 2008 campaign of Barack Obama, who energized the youth vote on his way to eight years in the White House. O'Rourke has drawn comparisons to Obama – including from the former president himself.

The invitation is the first sign since the election that O'Rourke, a three-term congressman, is being courted by influential New Hampshire operatives as a potential 2020 nominee for president. The group has not received a response yet from either Friedlander or O'Rourke, according to people with knowledge of the invitation.

The development comes after CNBC previously reported that O'Rourke's donors and supporters have been privately prodding him to run in 2020 for either president or against Texas' other GOP senator, John Cornyn.

New Hampshire's young Democratic leadership is excited for the possibility of seeing O'Rourke come to visit.

"When he's on the stump, it's engaging," Lucas Meyer, the organization's president, said in an interview. "When he speaks you're excited and you know he believes in it. You want to buy into that movement. That's why people are excited."

Top former advisors for Clinton and Obama have also been in touch with associates of O'Rourke to see where he stands on a run for the White House, according to two people with direct knowledge of the conversations.

Clinton's 2016 campaign manager, Robby Mook, has spoken with the congressman's close confidants about making a 2020 run and has said O'Rourke should if he wants to, these people said. Mook has also spoken with other 2020 hopefuls, but it's unclear who else he has engaged with.

Jeremy Bird, who worked as a strategist for both Clinton and Obama, has also spoken with O'Rourke's inner circle about his future, these same people said.

Mook and Bird did not return requests for comment.