Robert F Kennedy Jr is said to be considering New York Jets star Aaron Rodgers and the former pro wrestler Jesse Ventura as possible running mates.
Rodgers - who is also a conspiracy theorist and anti-vaccine campaigner - has reportedly been speaking "pretty continuously" to Kennedy Jr.
The nephew of former president John F Kennedy also said he was in touch with Minnesota governor Ventura after meeting him at an event in Arizona last month, the New York Times reports.
Kennedy Jr, 70, is running as an independent candidate in this year’s presidential election.
In response to the rumours, Ventura's son, Tyrel said: "No one has officially asked Gov. Ventura to be a Vice Presidential nominee so the Governor does not comment on speculation."
It remains unclear how Rodgers could combine a vice-presidential campaign with an intense NFL season that would clash with November's election.
The latest polling by The Hill shows Trump at 41.6 per cent, Biden at 38.6 per cent and Kennedy Jr at 11.3 per cent.
Kennedy Jr worked as an environmental lawyer before founding an anti-vaccine pressure group.
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Several running mate candidates have turned down Kennedy Jr, including Rand Paul, a Republican senator from Kentucky, and Tulsi Gabbard, a former Democratic congresswoman from Hawaii.
In addition, tech entrepreneur Andrew Yang, who failed in runs for the Democratic presidential nomination also shut down the role.
Paul told Politico: "I’m supportive of [Kennedy’s] ability to have a platform to speak out.
"I think he’s saying a lot of good things. But I have no plans to get involved in the campaign."
Ballot access rules for independent presidential candidates vary from state to state.
Some states require independents to choose a vice-presidential running mate before applying.
The Kennedy Jr campaign has so far qualified in four states - Utah, Nevada, New Hampshire and Hawaii.
