The Conservatives are to start a three-month leadership contest to replace Rishi Sunak this week, due to end with the announcement of a new Tory leader on 2 November.
Nominations will open on Wednesday, with candidates needing the backing of 10 MPs to enter the first round of voting.
MPs will narrow this down to four candidates, who will then have a chance to speak to party members at the Conservative conference which starts on 29 September.
MPs will then whittle those down to two candidates, with the final winner chosen by Conservative Party members in an online ballot.
Speaking to BBC Breakfast on Tuesday, shadow home secretary James Cleverly declined to comment on whether he would put himself forward in the leadership contest, but did not rule out the possibility.
He said he has been focused on "holding the new Labour government to account on my old portfolio, something that’s incredibly important, and that’s what I will be continuing to do, and we will see what happens once those nominations are open."
Pressed by BBC Breakfast, he agreed that his response was "not a no".
“The thinking that I and others will have done and will do about the leadership of the party is important and there is a timescale for that, and I’m not going to rush ahead of that timescale,” Mr Cleverly said.
When asked who he would support if he did not put himself forward as a candidate for leader, he said that was “tomorrow’s work”.
Mr Sunak's ally Mel Stride, the shadow work and pension secretary, has said he was "considering" announcing his candidacy for the race.
On Monday, Mr Sunak formally stepped down as leader of the Conservatives starting the process to elect his replacement.
He will remain acting leader of the party until a successor is appointed.
No-one has yet officially confirmed they will stand.
But other potential leadership candidates include former immigration minister Robert Jenrick, former home secretaries Suella Braverman and Dame Priti Patel, shadow security minister Tom Tugendhat and shadow communities secretary Kemi Badenoch.
The plans allow as many as 11 of the 121 surviving Tory MPs one week to file their nominations for the first round, which closes on 29 July.
Candidates will also be able to use the summer recess, starting next week, to mount their campaigns.
MPs will then begin narrowing down the field through a series of ballots when parliament returns in early September, reducing the field to four by the Tory conference at the end of that month.
The ballot of party members will close on 31st October.
Only members who have been a member for 90 days or more prior to the ballot closing, and have been an active member at the time of the nominations for candidates opening, will be eligible to vote, the party said.
The BBC understands Mr Sunak had wanted to stand down earlier, in order to allow the party to move on.
But it now looks like he could still be in post for Labour's first Budget - expected in the Autumn.
Mr Sunak said it was in "the national interest" for him to stay in post to allow "a smooth and orderly transition to a new leader of the opposition".
He said: “This will allow our party to fulfil its role as the official opposition professionally and effectively.
"I believe this is what is best for the Conservative Party and, most importantly, our country."
Bob Blackman, who as chairman of the backbenchers' 1922 Committee will oversee the selection of the new leader, said he was "determined that our party will have a respectful and thorough leadership debate".
He added: "While there are significant debates to be had about our party’s future, we must remember that the country - and our members - want to see us engaged in proper debate, not personal attacks."