The BBC debate would see the leaders take questions from a panel, as well as debating each other.
Mr Corbyn had agreed to debate with Mrs May over the Brexit withdrawal deal under the terms offered by ITV, but not those set out by the BBC.
Downing Street said it had accepted a proposal which would see the Brexit debate be screened on the BBC at 8pm on Sunday 9 December - two days before a crunch vote in the Commons.
The BBC's plan would see the leaders take questions from a panel, including commentators and politicians, as well as debating each other.
The Labour leader had said he preferred the ITV proposal involving a simple one-on-one format.
But in a tweet on Saturday, Mr Corbyn said: "Theresa May said she wanted a head-to-head debate with me on her botched Brexit deal and I am ready to do that.
"ITV have a straightforward plan. If she and her team prefer BBC, she should join me in asking them to arrange an actual head-to-head debate."
Earlier this week, the official Labour line was that Mr Corbyn doesn't want to stop audiences watching the I'm A Celebrity final.
Following Mr Corbyn's announcement that he is prepared to consider a BBC platform, the channel said: "Our proposal is to broadcast a programme which includes both a head-to-head debate between the prime minister and the leader of the opposition and also an opportunity to hear from a wider range of voices.
"After all, a broad range of views on this issue is held by the public and by parliamentarians - from those who want a different form of Brexit to those who want another public vote - and we believe that should be reflected in the debate."
Sky News has been campaigning for leaders' election debates to be overseen by an independent panel and our petition has gained more than 100,000 signatures.