The chairman of the highly influential European Research Group made the admission at a meeting of the group’s MPs in Parliament tonight, a source said.
His backing would be a huge boost for the Prime Minister’s twice-defeated deal as she seeks to build support ahead of plans to bring it back a third time.
But it could end up being of little use as the DUP remains bitterly opposed to the deal and seem highly unlikely to vote for it in its current form.
Mr Rees-Mogg was among a group of high-profile Brexiteers who met Theresa May at her Chequers country retreat yesterday.
He arrived with his eldest son Peter to the meeting in which he and others including Boris Johnson are believed to have urged her to set a timetable for her departure as PM.
Jacob Rees-Mogg arriving at Chequers yesterday with his eldest son Peter
Theresa May told the Commons today that she would not seek to hold a meaningful vote on her Brexit plan until he could get enough backing to pass it
But Mrs May showed no sign of heeding their desire today as she faced MPs in the Commons.
MPs are poised to vote on alternatives her Brexit deal this week - with rebels ready to seize control of the Commons agenda if the PM refuses to stage votes herself.
It is thought the Government could put up seven options to MPs if Mrs May accepts her deal has no hope in a third vote. The plan could be announced as soon as today following an emergency Cabinet.
The seven options are the existing deal, cancelling Brexit altogether, a new referendum, a Norway-style soft Brexit, a Canada-style hard Brexit, a UK-EU customs union or No Deal.
Backbench MPs have already warned the Government it must let MPs set out the possibilities to get a true sense of what the Commons might vote for.
A vote tonight could allow rebel MPs to seize the Commons agenda on Wednesday and stage their own indicative votes.
Mr Rees-Mogg' s fellow ERG member Daniel Kawczynski said he was recommending to its MPs that they back Mrs May.
The Shrewsbury MP tweeted: ‘Am addressing ERG now in Commons asking colleagues to support PM’s Withdrawal Agreement.
‘Unless we get behind this deal we could loose (sic) Brexit and I am not prepared to do that.
‘Shrewsbury voted for Brexit and we must deliver.’
Mr Rees-Mogg's fellow ERG member Daniel Kawczynski said he would urge its Brexiteers to back Mrs May in a new meaningful vote
The ERG plans to vote against all proposed changes to Prime Minister Theresa May's next steps on Brexit on Monday, a Conservative MP said tonight.
The lawmaker said the group planned to vote against the so-called amendments, including one which seeks to wrest control of the Brexit process to try to find a majority for an alternative that would break the parliamentary deadlock.
As long as the government's motion on its next steps is not amended, the ERG will vote for it, he added.
Mrs May caused fury among the DUP earlier for claiming No Deal preparations had been made in Northern Ireland because it has no devolved executive.
A No 10 spokesman insisted it was ‘not a tactic’ but a ‘statement of facts’.
The Prime Minister is keen to offer a final vote to stop MPs taking charge of the UK's departure from the EU with Parliament ready to push Britain towards a softer Brexit or a second referendum.
But a phone call between Mrs May and DUP leader Arlene Foster at lunchtime failed to provide the breakthrough the Prime Minister needs as she seeks to win support for her deal.
The 10 DUP MPs have opposed the Withdrawal Agreement in the two previous votes on it and a party spokesman said the party's 'position remains unchanged'.
Mrs May caused fury among the DUP - including its Westminster leader Nigel Dodds, above - earlier for claiming No Deal preparations had been made in Northern Ireland because it has no devolved executive
And in a sign of strained relationship the DUP's Westminster leader Nigel Dodds appeared to be shaking with rage as he accused Theresa May of a 'fundamental lack of preparation' for No Deal.
He said the Government had known for 'considerable time' the UK was due to leave the EU on March 29 - but still wanted an extension for a fortnight.
He said: 'What will change in 2 weeks?' before savaging her for agreeing to the Irish backstop 'when it is the thing that bedevils her agreement' and Ireland and the EU say the Northern Irish border will remain open in the event of a No Deal.
DUP MP Sammy Wilson then told Mrs May: 'When are you going to stop using Northern Ireland as an excuse? We will not be used in any scare tactics to boost this through.'