Prime Minister Theresa May has accepted the BBC’s offer to take part in a debate on Brexit on Sunday 9 December, two days before MPs vote on her deal.
But Labour sources say the party has not yet agreed to take part, with Jeremy Corbyn telling This Morning he preferred ITV’s offer.
The BBC said it was “delighted” Mrs May had accepted the offer.
It added it would be discussing debate formats with both parties and would announce further details soon.
Mr Corbyn claimed he preferred ITV’s bid because the BBC plan clashed with the final of I’m A Celebrity… Get Me Out Of Here!
“I want to watch it myself,” he said.
BBC assistant political editor Norman Smith said the BBC debate would include a panel of people involved in the Brexit debate who would be able to question the two party leaders.
He added Mrs May had accepted the offer “because there was a view on the government’s side that the BBC would address the crux of the issue, namely the deal”.
It is understood the BBC programme would be held on 9 December at 20:00 GMT in Birmingham, meaning it would replace David Attenborough’s Dynasties on BBC One.
By BBC political correspondent Chris Mason
Recent history tells us TV debates involving politicians are long in the gestation, and painful in labour.
Welcome to 2018’s anticipated arrival.
The BBC announces a debate is on – but there is a snag.
Jeremy Corbyn hasn’t said he will turn up.
He would rather go on ITV.
And so starts the posturing among the telly luvvies along the lines of “my audience is bigger than yours.”
There are other awkward questions for the broadcasters too: where is the passionate Brexiteer voice? Where is the advocate of another referendum?
Because even if Mr Corbyn accepts, the two biggest names on the programme wouldn’t be a million miles apart on the fundamentals.
It would be a discussion between two people who voted Remain and are committed to delivering Brexit, talking to an audience that doesn’t have a say on what happens next.
Oh and one last thought: this TV show, involving both of them, still might not happen.
The SNP, Lib Dems, Plaid Cymru and Greens have demanded to be involved to ensure a range of views is reflected.
Green MP Caroline Lucas tweeted that the debate should include dialogue “about all possible routes forward” – including another referendum.
Lib Dem leader Sir Vince Cable – who has also campaigned for a further referendum – said he was “raring and willing to go” in the TV debate, adding it would be a “travesty” if only Mrs May and Mr Corbyn were involved.
However, Mrs May has rejected calls for smaller political parties to join in, saying she and Labour leader Jeremy Corbyn represented almost 90% of MPs in the Commons between them.
Mrs May is beginning a two-week campaign to sell her Brexit deal to the public and MPs, before the vote in the House of Commons on 11 December.