A new survey of Tory Party members by the Conservative Home website has Brexit Secretary David Davis as favorite to take over from the hapless Theresa May, but Rees-Mogg, the MP for North East Somerset is the dark horse racing up on the outside.
A third of those who responded to the survey said "none of the above," when offered a list of Cabinet contenders including Home Secretary Amber Rudd and Chancellor Philip Hammond.
The vast majority of those picked Rees-Mogg as their choice and there is even a grassroots movement, dubbed Moggmentum in a dig at the Jeremy Corbyn-supporting Momentum movement, which is rooting for him.
While Rees-Mogg's pinstripe traditionalism has been the target of much ridicule on social media, betting markets place him second behind Davis.
In July, in an interview with Conservative Home, Rees-Mogg said he did not see himself as "a serious candidate" — although he regarded the prospect as "flattering" and did not explicitly rule out running.
So who is Rees-Mogg?
He is the son of William Rees-Mogg, who was editor of The Times newspaper in the 1970s and later vice-chairman of the BBC and a Conservative peer.
Jacob went to Britain's elite private school, Eton, and then read History at Oxford University before starting a career in the City of London.
He also worked in Hong Kong and in 2007 he co-founded an investment company, Somerset Capital Management, which now has a portfolio of US$7.6 billion and offices in London and Singapore.
In 1997, when Tony Blair's Labour Party won a landslide victory, Rees-Mogg gained only nine percent of the vote as the Tory candidate in the safe Labour seat of Central Fife in Scotland, where he was ridiculed for canvassing with a woman who was his nanny as a child.
In 2010, when he was elected as an MP, a Sunday Times columnist described him as "David Cameron's worst nightmare" because the new Conservative leader was desperately trying to shed the party's patrician image.
But while Cameron tried to play down his upper class roots, Rees-Mogg positively revels in it.
He has six children, and the latest he named Sixtus (after a Roman emperor) Dominic Boniface Christopher.
The others have equally upper class monikers — Alfred Wulfric Leyson Pius, Thomas Wentworth Somerset Dunstan, Peter Theodore Alphege, Anselm Charles Fitzwilliam and the rather more prosaic Mary Anne Charlotte Emma.
He is also on the right-wing of the Conservative Party.
Rees-Mogg is an ardent Brexit supporter, voted against same-sex marriage, opposed plans to scrap the bedroom tax, voiced support for Donald Trump and called for his party to collaborate with the UK Independence Party.
While Rees-Mogg's star is in the ascendancy, Davis' support fell from 24 percent to 20 percent, and Johnson saw his support drop from 19 percent to nine percent, his lowest rating since the survey began.