Peter Bone has said he is sceptical that the Prime Minister will announce her resignation date today.
Appearing on the breakfast show, the Conservative MP said there was "huge danger" in predicting what would happen in politics.
"I do think the Prime Minister will announce her resignation today and say the date when it will come into effect, but I wouldn't bet my house on it," he told talkRADIO's Alastair Stewart.
"The logic says today is when the Prime Minister says she is going to go, but logic has been lacking in politics for quite a long time."
Theresa May is meeting with 1922 Committee chair Sir Graham Brady this morning to discuss her leadership, and it is widely expected that she will announce a date in June to leave her role.
Discussing potential new party leaders, Mr Bone said he would be backing Boris Johnson.
"The Prime Minister I think has to be someone who is a leaver. I don't think it can be anyone who is in the current cabinet because they have gone along with this dreadful Withdrawal Agreement," he explained.
"It has to be someone who has resigned from cabinet, but it also has to be somebody who can walk into Downing Street the next day and be Prime Minister."
He continued: "The only conclusion you could have is that it has to be Boris. He fits all those criteria and nobody else does."
Mr Bone dismissed the idea of environment secretary Michael Gove as leader, and claimed that "most" members of the party had not forgiven the politician for "what he did to Boris" in the last leadership contest.
Michael Gove was accused of sticking a "knife" in the back of Boris Johnson after launching his own campaign to become Prime Minister despite being a long-time friend and colleague of the former Mayor of London, who was also in the running.