Chancellor Jeremy Hunt has already ruled out standing for the leadership of the Conservative Party after prime minister Liz Truss steps down.
Hunt will still deliver his fiscal statement as planned on 31 October, the BBC reports, despite the prime minister's resignation.
The government has to find an estimated £40bn of savings in the public finances.
Hunt, who ran in the last Tory race, said he no longer has any leadership ambitions. In an interview with the BBC on Sunday, he stated he would not run a third time.
“I think having run two leadership campaigns and, by the way, failed in both of them, the desire to be leader has been clinically excised from me.”
The South West Surrey MP was appointed the UK’s fourth chancellor in four months last Friday.
Speculation will be mounting over other contenders, including former chancellor Rishi Sunak, defence minister Ben Wallace, Penny Mordaunt and Suella Braverman, who resigned as Home Secretary only yesterday. Sunak is the current favourite along with Mordaunt.
Markets are predicting a Sunak leadership with Hunt by his side, something that would apparently calm market volatility.
"An initial bounce in the pound has begun to fade, as the implications of yet another period of uncertainty sink in. But given how quick the change is expected, and with the chancellor likely to stay in place, we should expect market tensions to calm," Chris Beauchamp, chief market analyst at IG Group, said.
In all likelihood Rishi is ready to step in, and with Hunt in alignment with him we can expect a very different approach, but one more likely to please markets," he added.
The chairman of the Tory 1922 Committee said he expected the new leader to be in place by next Friday.
Graham Brady said: "I have spoken to the party chairman Jake Berry and he has confirmed that it will be possible to conduct a ballot and conclude a leadership election by Friday, 28 October.
"So we should have a new leader in place before the fiscal statement which will take place on 31 October."
As prime minister for just 44 days, Liz Truss was the briefest serving PM in UK history. She will remain in No 10 until the Conservative Party chooses her successor.
Watch: Liz Truss resigns as Prime Minister