The Daily Mirror claimed the corporation had dropped the programme and that it could move to ITV.
A BBC statement said: "It is incorrect to say the BBC has axed The Voice.
"We are in discussions about its future, but we won't get into a bidding war." The fifth series of the show will start on BBC One in January.
Boy George, Paloma Faith will join will.i.am and Ricky Wilson on the judging panel.
The corporation has now made a "final" bid for two further series, which would run from 2017.
The BBC would not reveal how much it had bid, but it is understood to be unwilling to pay more than it did for previous series.
The show is currently made for BBC One by production companies Talpa and Wall to Wall. ITV bought Talpa for £355m earlier this year.
But the future of The Voice has become a political hot potato for the corporation as it negotiates with the government over its next royal charter.
The Voice was singled out in a consultation paper published by the government ahead of the BBC's charter renewal as a format that is "similar to ITV's X Factor", and which was bought in from overseas rather than being developed in-house.
Culture Secretary John Whittingdale has questioned whether such shows are "distinctive" enough from those aired by commercial rivals.
In August, the BBC's director of television Danny Cohen defended the corporation's right to air entertainment shows like The Voice.
"I believe that we should keep fighting for entertainment on Saturday nights on the BBC that reaches a wide range of people up and down the country, from all different sorts of backgrounds," he said.
"A show like The Voice, it's really popular with young people, diverse audiences and less well-off audiences and it matters to them as much as Strictly, and we should make sure that we offer both," said Cohen.
Doubts over the show's future mounted after Tuesday's announcement that Cohen is to leave the corporation.
The BBC has denied reports that it has axed The Voice UK, saying it has put in a bid to keep the talent show for another two series.