MPs have reportedly said the Chancellor should take over as Prime Minister before the Tory party conference in October, but only as a caretaker leader.
The ministers will reportedly ensure he only assumes the role for two years, so someone else can lead the party into the next election.
A former cabinet colleague told the Sunday Times that the Chancellor himself believes he is equipped to do the job.
In order to curb his ambitions for a soft Brexit, Tory insiders will reportedly beckon Brexit Secretary David Davis to become his deputy.
One Tory minister told the newspaper: “I think Philip is the only plausible candidate for a couple of years, with DD [David Davi]) running Brexit.
“He is a more credible caretaker than the current Prime Minister. The PM’s brand is so damaged it is painful.
“The calculation that people are beginning to make is that she is so inadequate we can’t wait two years with her in place.”
Mrs May’s reputation has been severely damaged after she failed to win a parliamentary majority in the last election, although she has only been leader for less than a year.
However, not all Tory ministers are backing Mr Hammond. Other cabinet ministers believe Mr Davis or Foreign Secretary Boris Johnson should take over.
Allies of Mr Johnson are said to be worried that a Hammond-Davis alliance would force the Foreign Secretary to put aside his leadership ambitions.
However, the Foreign Secretary has publicly vowed not to challenge May before Brexit is finalised in 2019.
Meanwhile Tory MPs who are friends with the Foreign Secretary claimed Mr Davis is too old to become Prime Minister because “he is nearly 70”, The Telegraph reports.
Discouraging a potential Davis leadership, one ally of Mr Johnson said: “People have short term memories. They see David as a steady hand but forget he lost to David Cameron in 2005 and has previously resigned.
“He’s also the man that pushed the Prime Minister into holding a snap election in the first place.
“Age is not a barrier but…