Sir Graham Brady, the chairman of the 1922 committee of backbench Conservative MPs, said it would be possible to conclude a leadership ballot by Friday next week.
He said he expected Conservative members to be given a say on who succeeds Ms Truss, but would set out further details later.
But he sidestepped questions about whether one or two candidates would be likely to run, telling reporters: “The party rules say there will be two candidates unless there is only one candidate.”
Candidates who contested the last leadership election earlier this year included Ms Braverman, International Trade Secretary Kemi Badenoch, Commons Leader Penny Mordaunt, and former Chancellor Rishi Sunak.
Their supporters are talking them up as potential candidates in the contest to succeed Ms Truss, but none have confirmed their position on standing.
Nor has former Prime Minister Boris Johnson, whose supporters have not denied reports that he is considering standing again for the Conservative leadership.
Lib Dems urge Tories to ban Johnson from standing for leadership again
The Liberal Democrats say the Conservative party should block Boris Johnson from standing again. In a statement the Lib Dem deputy leader, Daisy Cooper, said:
The fact that Conservative MPs are even considering putting Boris Johnson back in Number 10 shows how out of touch they really are. They think there’s one rule for them and another for everyone else.
Boris Johnson was forced to resign in disgrace after countless lies, scandals and failures. He shattered public trust in the government and plunged the UK into a political crisis. He must never be allowed near Downing Street again.
Yet another prime minister with no general election. No mandate. We used to laugh at Italy. Now the joke’s on us. The UK is far more chaotic, far more corrupt, than anything the Italians could dare dream of. Just 350 Tory MPs more concerned about holding on to their jobs for another two years than doing the right thing for the country. You’d laugh if it wasn’t so tragic and costly for the UK.
(with apologies to john crace)
