Robert F. Kennedy Jr. will announce the vice-presidential pick for his independent presidential bid at an event in Oakland, Calif., on March 26, his campaign said on Wednesday, a move that comes amid swirling speculation about his potential running mate.

The New York Times reported on Tuesday that the N.F.L. quarterback Aaron Rodgers and the former Minnesota governor and onetime pro wrestler Jesse Ventura were at the top of his shortlist, and that both had welcomed Mr. Kennedy’s overtures.

Mr. Kennedy confirmed the names to The Times on Tuesday, and said in an interview, “I would say we’ve already made a decision,” but he declined to provide details. In a text message on Wednesday, he said he had asked a candidate who had accepted the offer, but again did not elaborate.

Mr. Rodgers and Mr. Ventura were among at least a half-dozen potential candidates with whom Mr. Kennedy and his camp discussed forming a ticket.

Mr. Ventura’s son, Tyrel Ventura, told The Times late on Tuesday that the former governor had not been formally asked. On Wednesday, the younger Mr. Ventura said there had been no outreach “that I am aware of.”

A representative for Mr. Rodgers did not respond to several requests for comment. On Wednesday afternoon, Pat McAfee — a former professional football player who now hosts an ESPN podcast on which Mr. Rodgers is a frequent guest — said that Mr. Rodgers had heard the report of his vice-presidential consideration while in Costa Rica, at an ayahuasca retreat.

Use of ayahuasca, a natural hallucinogen, has become part of a growing trend of psychedelic retreats. Mr. Rodgers has praised the drug in the past for its “healing” properties.

Mr. Rodgers appeared in an Instagram video posted on Tuesday by Jordan Poyer, a veteran N.F.L. safety who signed on Tuesday with the Miami Dolphins. The post, which includes footage of a Costa Rica eco-resort, was cross-promoted by Behold Retreats, which bills itself as a service for guided experiences in psychedelic plant-based medicine.