The former London mayor was quoted as acknowledging there was no current vacancy with Prime Minister Theresa May still resident at 10 Downing Street.
Britain's tumultuous divorce from the European Union was again in disarray on Friday as the opposition Labour Party declared last-ditch cross-party talks dead as Prime Minister Theresa May's premiership crumbled.
It's now less clear than ever how the United Kingdom will leave the European Union, three years after Britons gave a narrow mandate for the split in a bitterly fought referendum. The latest deadline agreed with the European Union is October 31, but there now seems little prospect of any plan winning a majority in the House of Commons.
In the Thursday meeting with the 1922 Committee, an influential group of Conservative lawmakers from her own party, the prime minister agreed to step down if her Brexit deal is voted down when she brings it to the House of Commons in the week beginning June 3.
Labour Party leader Jeremy Corbyn said that "we have been unable to bridge important policy gaps between us". Mr Corbyn said with a Tory leadership battle now weeks away he has no "confidence" in the "Government's ability to deliver any compromise agreement" and said later: "She is not going to be Prime Minister for much longer anyway".
"We have agreed that she and I will meet following the second reading (first vote) of the bill to agree to a timetable for the election of a new leader of the Conservative and Unionist Party", he said.
Across the channel, Dutch Prime Minister Mark Rutte told reporters that "the whole concept of Brexit is wrong", in reference to the talks' breakdown.
"There are only two ways out of the Brexit crisis that we've got: either parliament agrees a deal or we go back to the British people and ask them to make the choice".
A source in May's office said the bill would not be the same thing parliament had rejected and will contain new features to reflect some lawmakers' concerns.
The pound sank to $1.275, its lowest level since mid-January.
May's hands have been tied, knowing that to make concessions to Labour would lead to fury in her divided party.
The Government will now focus its efforts on trying to win over rebel Tories and the DUP, while hoping that Labour MPs can be persuaded to back the WAB based on the common ground established during the talks on areas including workers' rights and environmental protections.
The Brexit impasse is unlikely to be broken swiftly. The vote is not binding, but if May has not set a date for her departure by then it will add to the pressure for her to do so. Many blame May and want her replaced with a more staunchly pro-Brexit leader, such as former Foreign Secretary Boris Johnson.
"The Brexiteer candidates (ie Boris [Johnson] and Dominic Raab) in particular should be very careful what they say during the campaign - temptation clearly to talk tough, but probably odds on that their first action will have to be requesting another extension from the European Union".
He's confirming that cross-party talks are now over and both sides will have to find a new way to move forward in this whole Brexit ordeal.