A number of Conservative members have reportedly been sent more than one ballot paper for the leadership election.
It added those affected could include people who joined their local Conservative party at their home and work address or others who have changed their name.
The party told the broadcaster members will be clear that anyone voting twice will be expelled.
Former Cabinet minister Sir Patrick McLoughlin, who is chairing Hunt’s campaign, said the issue has “got to be looked at” but said he expected Tory members to follow the rules and vote just once.
Sir Patrick, a former Conservative chairman, told the BBC’s Today programme: “It’s made very clear on the ballot paper that you are only allowed to vote once. I expect Conservative members to follow that.
“If people have joined two associations they may get two ballot papers. I get two ballot papers in elections because I am on two different sets of electoral registers, it doesn’t mean that I vote twice, I don’t.”
He added: “It can’t be clearer, it’s right there on the ballot paper saying that you must only vote on one occasion and I expect people to do that”.
The vote closes on July 22 and the result will be revealed a day later.
Theresa May will take her final session of Prime Minister’s Questions on July 24 and hand over to the contest winner that afternoon.