Rishi Sunak is being urged to delay quitting as Tory leader until a successor is chosen in the autumn.
The former Prime Minister has said that he would stand down from the helm of the Conservative Party once the plans to elect the next leader are in place.
But senior Tories are keen for him to stay on for longer so they can avoid having to appoint an “interim leader”.
They also believe that the new MPs, some two dozen, should be able to see how the different leadership contenders perform at the Despatch Box in Opposition, before having to make a choice, given that it requires different skills to being a minister.
Some senior Conservatives are pushing for a similar leadership contest as used by outgoing Tory leader Michael Howard in 2005 which saw David Cameron chosen.
It would mean final leadership hustings at the autumn party conference in Birmingham, which runs from September 29 to October 2, and then MPs voting to create a shortlist of two candidates on their return to Parliament, before the final choice was made by party members.
On July 5 after the crushing election defeat for the Tories, Mr Sunak said in his Downing Street departure speech: “Following this result, I will step down as party leader - not immediately, but once the formal arrangements for selecting my successor are in place.“
But shadow foreign secretary Andrew Mitchell stressed: “An interim leader is not, in my view, the best option. The best option is to seek to persuade Rishi to remain. It’s not an enormously long time in the scope of things. It’s probably till mid to end November.
“And while I completely understand his possible reticence, I hope very much the feelings of goodwill towards him, which were expressed at the meeting of the 1922 committee last week...”
Speaking on Times Radio, Mr Mitchell added: “I think his instinct is almost certainly to go. I hope that he won’t. I hope he will stay till November for the reasons that I have described.
“And at the 1922 committee meeting last week, there was a widespread feeling of sympathy and respect for Rishi Sunak. And I'm sure that if he does stay, that will be the overwhelming feeling of the party."
No candidate is yet to official declare they will run for the Conservative leadership.
But some candidates are already privately contacting prominent Tories to seek their backing.
Those expected to run include ex-Business Secretary Kemi Badenoch, former Home Secretaries Dame Priti Patel, James Cleverly and Suella Braverman, former immigration minister Robert Jenrick, and ex-security minister Tom Tugendhat.
Former Mayor of the West Midlands Andy Street has warned his party against a lurch to the Right, while Mr Cleverly has stressed that it needs to “get its act” together.
Polling by the ConservativeHome website found Ms Badenoch, who has clashed publicly with Ms Braverman, is currently the leadership favourite.
Its survey showed the former minister for women and equalities had the support of 25.83 per cent of grassroots Tories.
Former immigration minister Mr Jenrick was second favourite, with 13.47 per cent support.
Former International Development Secretary Mr Mitchell believes the Tory Party should take its time in choosing its next leader.
“I very much hope that what the party will decide to do is to mirror what Michael Howard did in 2005 and allow the party conference the space for candidates who are offering themselves to say what they would do for their party, say what they would do for their country, and that members of the party, Members of Parliament can then take a view as a result of that showcasing,” he said.
“But I don’t think it should be hurried. And I think we should have a long, careful look at who is the right person now to lead his Majesty’s Opposition.
“The Conservative Party will provide in Parliament a highly responsible and proper, effective scrutiny of the government because everyone knows that good governments are improved by good scrutiny. And that’s what we will try to provide.”
