The PM’s plan would reportedly offer cash injections for deprived areas which backed Brexit in the 2016 referendum.
Mrs May is battling to win a majority for her Brexit deal amid fierce opposition from many of her own Conservative backbenchers.
Number 10 aides believe the backing of 20 Labour MPs could be enough to take a Brexit deal over the line to avoid a cliff-edge exit on March 29,
Theresa May (pictured) will persuade Labour MPs to back her Brexit deal by offering money for their constituencies, it has been claimed
A Government source told the newspaper: ‘There’s a willingness to look again at coalfield communities and make good the promises that former Labour governments failed to deliver.
‘It’s about allowing Labour MPs representing Brexit communities to show that they have extracted something tangible in return for their vote.’
Fourteen Labour rebels broke with Jeremy Corbyn to block a proposed Brexit delay in a Commons vote on Tuesday night.
Seven of them also voted with the Tories to back the Brady amendment calling for changes to the Irish backstop.
Tuesday’s Commons vote demanded the replacement of the backstop with ‘alternative arrangements’ to avoid a hard border on the island of Ireland.
Mrs May is due to report back to Parliament on her negotiations with the EU on February 13, with a further series of votes by MPs expected the following day.
European Commission president Jean-Claude Juncker, pictured in Brussels yesterday, rejected the call by MPs for the Brexit deal to be renegotiated
But her plan to rewrite the deal has met a wall of resistance from the EU, with the continent’s most senior politicians and officials lining up to insist the deal cannot be unpicked.
European Commission president Jean-Claude Juncker described the Agreement reached after 18 months of negotiation last November as ‘the best and only deal possible’.
Mr Juncker said he would stay in close contact with Mrs May and would ‘listen to her ideas’.
Having boycotted earlier cross-party talks, Labour leader Jeremy Corbyn said he was ready to discuss a ‘sensible’ approach to Brexit after MPs voted on Tuesday night to rule out no deal.
Following the meeting, Mr Corbyn said he is ‘suspicious’ that Mrs May is trying to ‘run down the clock’ on Brexit.