Currently the unionist party is refusing to support the agreement, which it claims would separate Northern Ireland from the rest of the UK.
However Cabinet Ministers are holding talks with the DUP in a bid to change their mind.
The Government is currently dependent on the DUP for its Parliamentary majority.
According to The Telegraph Government sources have indicated the Party could be offered additional funding for Northern Ireland, in return for backing the exit deal.
Following the 2017 General Election over £1billion was allocated to Northern Ireland, one of the poorest parts of the UK, after the DUP agreed to support the Conservative Government in Parliament.
The DUP’s Westminster leader Nigel Dodds has held talks with senior Government figures.
These included Chancellor Philip Hammond, Environment Secretary Michael Gove as well as the Government’s chief whip.
However Mr Dodds insisted his party has not been offered money in return for its support.
He commented: “We are not discussing cash in these discussions.
“From day one, our focus has been on the red line of how Northern Ireland is treated separately from the rest of the UK.
“That is the issue that has been the priority concern for us.”
The DUP joined Tory rebels in voting down Mrs May’s Brexit deal on Tuesday by a margin of 149 votes.
They also opposed it during the first ‘meaningful vote’ in January, which was defeated by a record margin of 230.
DUP leaders are concerned the Brexit agreement could weaken the union between Northern Ireland and the rest of the UK.
Should the party change its position it could have a significant impact on Conservative opponents of the deal, potentially persuading them to change their votes.