Speaker Michael Martin was elected to the role in 2000
He will make an announcement at 2:30pm when he opens the Parliamentary session.
Mr Martin is still due to meet party leaders to discuss reform of MPs' expenses at 4:30pm.
Prime Minister Gordon Brown said it was for the Speaker to tell the Commons what his intentions are.
"It is only fair to wait until he says that," he said. "It is not for the Prime Minister to tell the Speaker what to do.
"The Speaker will make his own statement and I will comment on what he has said after he has made his statement."
The Speaker has been under pressure over the issue since last year when he fought, in court, to keep MPs' expenses claims secret.
When the details were released by the Telegraph, he angered MPs by appearing more concerned with finding out how they were leaked than with their contents.
Yesterday Tory MP Douglas Carswell tabled a motion of no confidence in Mr Martin but the Speaker refused to allow MPs to ask questions about it.
Adam Boulton, Boulton & Co.
He told the public and the Commons he was "profoundly sorry" for his role in the affair but said the motion could not be debated because it was not "substantive".
Extraordinary scenes followed as a series of MPs rose to demand he stand aside or submit to a vote of no confidence.
Sky's political correspondent Joey Jones said: "I think the likelihood is that friends of Michael Martin will have told him to think about the situation and to consider the events of yesterday, when he had no control of the House of Commons.
"He will have reflected on that overnight.
"I am sure that he will have taken counsel from his fellow MPs, perhaps particularly among the Scottish MPs, and decided that this was the time to go."

Mr Carswell told Sky News it gave him no pleasure to have played a part in bringing Mr
Martin down, but said the House of Commons needed a new Speaker to help guide it out of the current crisis.
The Harwich and Clacton MP said: "I have acted not as his enemy and least of all as an opposition MP. I have acted as somebody who cares passionately for the parliamentary system.
"I believe we have found ourselves in a moral ditch and we need reform and change to get out of that ditch and restore dignity to politics."
Text of Mr Carswell's motion of no confidence in the Speaker
Mr Martin was widely denounced for allowing police into the Palace of Westminster to search senior Tory Damian Green's office last year.
Several MPs broke convention by publicly suggesting he should stand down, on the grounds that he could no longer be relied on to protect their rights.
Mr Martin was forced to take the unusual step of making a statement to the House, saying the police had neither a search warrant nor his permission to raid Mr Green's office.
He laid the blame on Serjeant-at-Arms Jill Pay, who he said had "regrettably" granted permission without his explicit say-so.