The Home Secretary only had 2 percent support from those polled by website ConservativeHome three months ago, but now has 22 percent support from the 1,107 votes cast by Tory supporters.
Mr Gove, the Environment Secretary and the arch-Brexiteer backbencher Mr Rees-Mogg are now ranked second and fourth respectively whereas Boris Johnson is only in fifth place.
The astonishing poll and turnaround for the Health Secretary comes after reports senior figures in Theresa May’s Government are on maneuvers in preparation for a leadership battle.
However, two senior Tories have urged ministers to fall in line behind the Prime Minister or risk putting on hold talks with the European Union.
Sir Graham Brady – who chairs the 1922 Committee of backbench Conservatives – wrote on the Observer: “The danger of disunity at the top of the party is not just that it makes the Prime Minister’s job more difficult in negotiations with Brussels, and therefore puts at risk the good Brexit deal that is in reach.
“It also gives an impression of division to the country.
“Electorates these days are volatile, but one thing is certain: they do not vote for divided parties.
“They rejected decisively the divided Tory party in 1997.
“If we were to let Labour in again, it would be a disaster for this country.”
The cry for unity was also echoed by Damian Green, who said we should show a united country now more than ever.
Mr Green urged in the Times on Sunday: “It is vital that as a country we show as united a front as possible at this key stage of the negotiations.
“We all know the divisions that Brexit has caused and there is no point disguising them. Certainly the Europeans know about them very well.
“But it is not too much to ask that the Government itself can show a united front in the national interest.
“That means that every individual minister has a responsibility to think about his or her own public words, and decide whether now is the right time to be parading some individual hobby horse.”
In the meantime, the Health Secretary’s team said to have begun consulting special advisers in other departments to join his top team if he makes it to Number 10.
Health Secretary Jeremy Hunt was also reportedly seen inviting MPs to lunches in Parliament.
Defence Secretary Gavin Williamson is currently in a battle with Theresa May’s Government over military spending and is planning to enlist the support of the Royal family to persuade Number 10 to give more money to the armed forces.