Theresa May is taking a commanding lead in the Tory leadership contest, with the home secretary thought to be able to count on the backing of six out of 10 Conservative MPs.
Rival candidate Michael Gove is facing bitter recriminations over his decision to back out of supporting Boris Johnson, which appear to have dented his prospects.
Separately, out of 139 MPs who have spoken to ITV News, 82 said they would be supporting Mrs May.
The Sun on Sunday's poll had Mr Gove as second on 10 points and Andrea Leadsom, the energy minister, on six.
But support for Ms Leadsom, who like Mr Gove campaigned for Brexit, is growing and the Justice Secretary faces being pushed into third place.
In an interview with the Sunday Telegraph, former City worker Mrs Leadsom likened herself to Margaret Thatcher and praised the late prime minister's ability to mix toughness with "personal warmth".
"I think that's an ideal combination - and I do like to think that's where I am," she said.
Ms Leadsom also told the paper that she had a fast-track policy for leaving the EU and that under her leadership Brexit could be complete as early as next year.
Meanwhile, Mr Gove wrote in the same paper of how he had been forced to "put friendships aside" and stand as party leader, despite having said on several occasions in the past that he was not interested in the job.