None have formally declared their candidacy.
TRUSS QUITS
Truss quit on Thursday after the shortest, most chaotic tenure of any British prime minister after her economic programme shattered the country's reputation for financial stability and left many people poorer.
Truss said she could no longer carry out her programme after her economic plan roiled markets and ended up on the cutting room floor when she was forced to bring in a new finance minister.
"I have therefore spoken to His Majesty the King to notify him that I am resigning as leader of the Conservative Party," said Truss, who was supported only by her husband with her aides and loyal ministers noticeably absent.
The sight of yet another unpopular prime minister making a resignation speech in Downing Street - and the start of a new leadership race - underscores just how volatile British politics has become since the 2016 vote to leave the European Union.
Some Conservative lawmakers hope the race to replace her will be quick and simple, urging the hopefuls to coalesce around one candidate to reduce the pain of another bruising contest.
Sunak, proven right in his warnings that Truss's fiscal plan threatened the economy, is the favourite but remains deeply unpopular with some Conservatives after he helped to trigger the summer rebellion against Johnson.
Mordaunt is seen as a fresh pair of hands largely untainted by earlier administrations. But she is also untested and, so far, she is lagging Sunak and Johnson in getting backers.
Whoever takes over the party, they have a mountain to climb to try to restore or renew the reputation of the Conservative Party, which holds a big majority in parliament and need not call a nationwide election for another two years.
"Whether or not a change of leader is going to be sufficient to make the Conservatives actually electorally credible is certainly highly debatable," political scientist John Curtice told LBC.
"The problem for the Conservatives is that the brand of them as a party that can mind the economy ... has now been very, very badly tarnished, and it may be very difficult to recover within the space of two years."