Robert F Kennedy Jr, a leading voice in the anti-vaccine movement, says President-elect Donald Trump has asked him to chair a study on vaccine safety.
Incoming White House Press Secretary Sean Spicer confirmed the pair met to discuss vaccines and immunisations.
However, a spokeswoman for Mr Trump, Hope Hicks, told Reuters that "no decisions have been made at this time".
Mr Kennedy has long contended that some vaccines may cause autism, a claim that has been widely debunked.
The president-elect has also expressed doubt about vaccinations.
"I am totally in favour of vaccines," Mr Trump said in a 2015 Republican primary debate.
"But I want smaller doses over a longer period of time. Same exact amount, but you take this little beautiful baby, and you pump - I mean, it looks just like it's meant for a horse, not for a child, and we've had so many instances, people that work for me. ... [in which] a child, a beautiful child went to have the vaccine, and came back and a week later had a tremendous fever, got very, very sick, now is autistic."
Medical experts have overwhelmingly rejected any link between vaccines and autism, warning that promoting such a theory endangers public health.
The Centers for Disease Control and Prevention has found no connection between autism and vaccines, citing numerous studies.
The commission will focus on making "sure we have scientific integrity in the vaccine process for efficacy and safety effects," Mr Kennedy told reporters after Tuesday's meeting at Trump Tower in New York.
Mr Kennedy, the eldest son of liberal icon Senator Robert Kennedy, is an environmental activist who has focused his attention on the "anti-vax" movement. He campaigns for parents to opt out of vaccinations and immunisations.
He came under fire in 2015 for describing the number of children injured by vaccines as "a holocaust" during a film screening of Trace Amounts, a documentary on the subject.
Mr Kennedy later apologised and said he "struggled to find an expression" to convey his thoughts.
Analysis - By James Gallagher, health and science reporter
Mr Kennedy's potential appointment has already been described as "very frightening" by one scientist.
The link between the MMR (Measles Mumps and Rubella) vaccine and autism has been thoroughly discredited.
The British doctor Andrew Wakefield - who first suggested the link - can no longer practise medicine in the UK after being struck off for acting "dishonestly and irresponsibly".
So the rise of a prominent anti-vaxxer can be seen as a massive middle-finger to established science.
However, this is not a surprise.
Andrew Wakefield remains vocal in the US and during the election campaign he met Mr Trump.
Afterwards he told the science news website Stat: "For the first time in a long time, I feel very positive about this, because Donald Trump is not beholden to the pharmaceutical industry."