Mrs May will confirm her decision in an exchange of letters with the joint acting chairmen of the backbench 1922 Committee, Charles Walker and Dame Cheryl Gillan.
A call for candidates will then be issued at 5pm, with nominations opening at 10am on Monday and closing at 5pm the same day.
The reported row comes after Downing Street defended the need for ambitious action to tackle climate change following warnings from the Treasury that cutting the UK's greenhouse gas emissions to zero by 2050 will cost £1 trillion.
Even as the formalities around Mrs May's departure were taking place, the 11 contenders so far to declare in the race to succeed her were engaged in increasingly bitter exchanges.
Former Brexit secretary Dominic Raab was at the centre of a political storm after he suggested he could be prepared to suspend Parliament to prevent it blocking a no-deal Brexit on October 31.
Home Secretary Sajid Javid became the latest contender to denounce the idea - branding it "anti-democratic and anti-British".
Speaking to the British Future think tank on Thursday, Mr Javid said that while he wanted to leave the EU by the cut-off date of October 31, he accepted Parliament was entitled to a say.
"I wouldn't prorogue Parliament. That is a complete nonsense. My policy would be to do everything I can to leave the European Union on October 31," he said.
"If it got to a point where I had to choose between no deal or no Brexit, I would pick no deal. But whatever I do, Parliament is going to want have its say on it and Parliament should have its say.
"Our Parliament is sovereign. I am not into this proroguing Parliament rubbish. It is just a complete nonsense and anti-democratic and anti-British."
Mr Javid also took a sideswipe at leadership front-runner Boris Johnson over his comments last year saying Muslim women who wear the burka looked like letter boxes.
"I think they they are wrong. I don't think they are the right comments. I don't think any serious politician should use language like that," he said.
Meanwhile, Michael Gove received a boost as Tory Party vice-chairman Kemi Badenoch announced she was quitting her post at Conservative headquarters to join his campaign.
Writing in The Sun, she said she was supporting the Environment Secretary because she believed he could deliver on the 2016 referendum result.
"Anyone can make promises. It is no good just believing in Brexit if you can't actually deliver," she said, in a clear dig at his rivals like Mr Raab.
"I'm suspicious of anyone proposing simple answers - shutting down Parliament until no deal, a snap general election, or an immovable Brexit deadline.
"If there were simple solutions they would have been tried already."