Robert F. Kennedy Jr. has recently approached the N.F.L. quarterback Aaron Rodgers and the former Minnesota governor and professional wrestler Jesse Ventura about serving as his running mate on an independent presidential ticket, and both have welcomed the overtures, two people familiar with the discussions said.

Mr. Kennedy confirmed on Tuesday that the two men were at the top of his list. It is not clear if either has been formally offered the post, however, and Mr. Kennedy is still considering a shortlist of potential candidates,the people familiar with the discussions said.

Mr. Kennedy said that he had been speaking with Mr. Rodgers “pretty continuously” for the past month, and that he had been in touch with Mr. Ventura since the former governor introduced him at a campaign event last month in Arizona.

A representative for Mr. Rodgers did not immediately respond to a request for comment. Mr. Ventura’s son, Tyrel Ventura, said in an email message late Tuesday: “No one has officially asked Gov. Ventura to be a vice-presidential candidate so the governor does not comment on speculation.”

The involvement of Mr. Rodgers — who is expected to start for the New York Jets this fall, at the height of campaign season — or of Mr. Ventura could add star power and independent zeal to Mr. Kennedy’s outsider bid.

Polls show Mr. Kennedy pulling roughly equal numbers of votes away from both President Biden and former President Donald J. Trump — but Democrats are far more worried than Republicans that he could tilt a close election to Mr. Trump. Mr. Biden’s allies have been working to block Mr. Kennedy from the ballot across the country.