The Mail on Sunday has reported that MPs approached to give their support to Adam Afriyie as a potential successor to David Cameron had been told that Mr Afriyie had the backing of 40 MPs.
The Sunday Times quoted a "friend" of Mr Afriyie, who is 47, as saying: "The team are well organised.
"They are very concerned about the long-term future of the party and believe Adam is the future. He has a fantastic back story and is very impressive."
More top news
Two ambulances crashed leaving one driver dead and three people seriously injured.
A scandal-hit NHS trust where a teenager drowned in the bath is still failing to protect patients from risk of harm, a watchdog has found.
New research suggests metal-on-metal hip replacements implanted since 2006 are more prone to failure and they "fail in a much nastier way".