The senior politician told the BBC: “Don’t believe all those things you read in the newspapers and take it that there are a lot of numbers behind the noise.
“And that’s where you need to apply a lot of political judgment to work out whether the complainers are just a fringe, or whether they represent the main body of opinion in the middle.
“The main body of opinion in the middle and right to the edges is absolutely solidly behind her.
“Because the idea that we can go for anybody else at the moment is just folly. It would lead to collapse and disarray.
“It’s not a credible option.”
Sir Alan also took another swipe at his former boss at the Foreign Office Boris Johnson, saying: “I think support for Boris politically has always been exaggerated over the last two years.
“But, he’s a great media phenomenon.
“And, so wherever he goes there’s a media crush.
“But, that’s not the same as someone who should be running the country.”
Mrs May is under pressure from some members of the Tory party following growing frustration of some MPs who openly say their party is directionless.
Conservative lawmaker James Duddridge said he had submitted a letter to the party’s so-called 1922 committee, calling on the Prime Minister to resign just minutes before her conference speech.
Forty-eight lawmakers would need to write such letters to trigger a vote of confidence.
Mr Duddridge wrote on Twitter: “Turns out there is a plan. That plan is Boris.”
Former Foreign Secretary Mr Johnson last week branded Mrs May’s Chequers plans a “cheat” and gave a wholehearted speech at the Tory conference on her handling of Brexit.
“If we cheat the electorate – and Chequers is a cheat – we will escalate the sense of mistrust,” Mr Johnson declared.
He also warned: “And I am afraid we will make it more likely that the ultimate beneficiary of the Chequers deal will be the far-Right in the form of Ukip.”