Mr Bercow has played a controversial role in the Brexit process frustrating the Government on multiple occasions. In March he passed a ruling making it harder for MPs to vote on Mrs May’s Brexit deal a third time. He has also been accused of prioritising amendments which are designed to undermine or soften Brexit.
According to the Mail on Sunday Mr Bercow put on hold plans to resign following “huge pressure” from Europhile parliamentarians.
A source told the paper Mr Bercow had “listened closely” to requests from several Conservative and Labour MPs to remain in post.
These are said to have included Conservative MPs Dominic Grieve, Ken Clarke and Oliver Letwin as well as Labour representatives Yvette Cooper and Hilary Benn.
All five politicians have previously advocated either watering down on cancelling Brexit.
The source commented: “The MPs have put him under huge pressure not to leave the Chair until Brexit is sorted.
“He is now unlikely to give any hint of his going until after the summer recess at the earliest, and may well wait to see if the new October 31 deadline is met before hanging up his boots.
“Ken Clarke, who John Bercow listened to more than any other MP, was a particularly decisive voice, telling him that it was his duty to stay.”
If the current Speaker does remain in post he could potentially face a no-confidence motion tabled by Brexit backing MPs.
It has also been suggested that Mr Bercow might not be given a peerage after he resigns, in a move which would break with a 230 year old tradition.
According to the Mail on Sunday Mr Bercow had been planning to go on a speaking tour of America this summer.
Theresa May agreed on Wednesday to postpone Brexit until October 31, unless MPs pass her EU exit plan.
She is currently negotiating with Labour to seek a Brexit plan that can pass the House of Commons.