The New York Jets quarterback Aaron Rodgers and the former pro wrestler and Minnesota governor Jesse Ventura are at the top of Robert F Kennedy Jr’s list of potential running mates for his independent presidential campaign, the New York Times reported.

Kennedy told the paper he was speaking to Rodgers – a fellow conspiracy theorist and anti-vaccine campaigner – “pretty continuously” and had been in touch with Ventura since being introduced by him at an event in Arizona last month.

Rodgers did not immediately comment. Ventura’s son said his father “does not comment on speculation”.

Democrats fear Kennedy, 70 and the son of the assassinated US attorney general and New York senator Robert F Kennedy, could prove a spoiler in Joe Biden’s rematch with Donald Trump.

Polling gives Kennedy a positive favorability rating with voters, a luxury denied to Biden and Trump. A polling average compiled by the Hill shows Trump at 41.6%, Biden at 38.6% and Kennedy at 11.3%. Democrats have worked to keep Kennedy off ballots in key states.

In Kennedy’s search for a running mate, those who have turned him down include Rand Paul, a Republican senator from Kentucky; Tulsi Gabbard, a former Democratic congresswoman from Hawaii; and Andrew Yang, a tech entrepreneur who failed in runs for the Democratic presidential nomination and for the mayoralty of New York City.

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.”

Gabbard is widely thought to be courting Trump. Politico said she had stopped cooperating with Kennedy’s vetting committee.

Kennedy is an environmental lawyer and campaigner whose turn to conspiracy theorising and vaccine scepticism has stoked controversy and rebukes from his famous family. Last month, he apologised for – but kept promoting – a Super Bowl spot based on a famous ad for his uncle John F Kennedy’s victorious 1960 presidential campaign.

Rodgers made his name with the Green Bay Packers, winning the Super Bowl in 2010. Now 40, his move to the Jets began with a serious achilles tendon injury. A familiar media presence who even auditioned to host the gameshow Jeopardy!, Rodgers last week responded to Kennedy’s response to Biden’s State of the Union address by saying: “This is presidential.”

Like Kennedy, Rodgers has stirred controversy with conspiracy-laced opinions about Covid-19, masking and vaccines.

He has also said he has used psychedelics to help his NFL career.

“Is it not ironic,” he said last year, “that the things that actually expand your mind are illegal and the things that keep you in the lower chakras and dumb you down have been legal for centuries?”

In 1999, critics who could not know what was coming next, in the form of the Tea Party and Trumpism, bemoaned Ventura’s election as governor of Minnesota on the Reform party ticket as evidence of a dumbing down of US politics.

A Vietnam veteran and member of the WWE Hall of Fame, Ventura left the Reform party in office. Since stepping down as governor in 2003, he has often flirted with third-party runs for Congress or for president.

Like Kennedy, Ventura has written for the Guardian. In 2013, he wrote about his admiration for Robert F Kennedy Jr’s uncle, the 35th president who Ventura said “brought us away from the brink of death and destruction” in the Cuban missile crisis, “by standing up to the war mongers and allowing sanity to prevail”.

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