Raab – the former Brexit secretary – has been tipped to take over as Tory leader by bookies Betfair.
The MP for Esher and Walton quit the Cabinet last month in opposition to Mrs Mays plans for Brexit.
He slated the PMs handling of the deal, calling it worse than remaining in the EU.
May's leadership is on the line tonight when Tory MPs participate in a vote of no-confidence amid fury over Brexit.
The PM backtracked on a “meaningful vote” for the House of Commons on her deal amid fears it wouldnt pass through Parliament – before scurrying back for further talks with the EU.
“Dominic Raab looks the man to step into Number 10”
Betfair spokeswoman Katie Baylis
Raab, 44, was seen as a relative newcomer to the top table of government – and has odds of 9/2 to be the next leader of the Tories.
He had served in junior ministerial roles since being elected in 2010.
The MP campaigned for Brexit ahead of the 2016 referendum on Britain's EU membership and is a black belt in karate.
And he was previously tipped by Brexit supporter Jacob Rees-Mogg as a prime successor to May.
FAVOURITE: Dominic Raab leaves his home this morning amid chaos in Westminster (Pic: REUTERS)
Sajid Javid and Boris Johnson are joint second place – both at 5/1.
Javid, 48, would be a successor to Mays agenda, while Johnson, 54, has been considered PM in-waiting since the EU Referendum.
Former foreign secretary Johnson is May's most outspoken critic over Brexit.
And the current home secretary Javid voted remain in referendum, and consistently polls well with Tories.
ALLY: Sajid Javid is seen as a natural successor to Theresa May's agenda (Pic: GETTY) Related Articles
CRITIC: Boris Johnson has been open in his criticism of Theresa May (Pic: PA)
Cabinet heavyweights Michael Gove and Jeremy Hunt – the environment and foreign secretaries – come in 6/1 and 7/1.
Gove has become a surprise ally to May after he teamed up with Boris during the referendum to campaign against the government in favour of Brexit.
He pulled his support from Johnson at the last minute – scuppering the former Mayors bid, and laying out his own stall to be PM.
Hunt remains unpopular with the public after serving six years as health secretary – but has called for party unity amid the chaos over Brexit.
OUTSIDER: Michael Gove has become a surprise ally of Theresa May (Pic: REUTERS)
Brexiteers David Davis and Jacob Rees-Mogg both come in as distant contenders at 9/1 each.
Davis was the inaugural Brexit secretary, and quit the government during the summer in protest of Mays deal with the EU.
Rees-Mogg meanwhile has called on the PM to quit, and is the chairman of the powerful European Research Group – a cabal with the Tories campaigning for a harder Brexit.
He is popular with fringe wings of the party for his charisma and Downton Abbey persona, and could be regarded as the architect of current efforts to depose the PM.
THROWBACK: Jacob Rees-Mogg has been an open critic of Theresa May and masterminded the coup (Pic: REUTERS)
Betfair spokeswoman Katie Baylis said: “While Theresa May is under immense pressure to retain the leadership ahead of tonights vote, we are seeing a huge amount of backing from punters since the vote was announced this morning for her to prevail.
“Shes now odds-on at 1/2 to come through tonight with her leadership still intact, and those odds have been shortening by the minute.
“However if she was to lose the vote, Dominic Raab looks the man to step into Number 10 and is the 9/2 favourite to take over, with Sajid Javid at 5/1, alongside Boris Johnson whose odds have slightly shortened this morning.”
Mrs May faces the vote tonight between 6pm and 8pm – with Brexit just 107 days away on March 29.