May was forced to quell a rebellion on Tuesday after she faced defeat on a vote in parliament over her Brexit blueprint, or EU withdrawal bill, which will sever ties with the European Union.
Several pro-EU lawmakers threatened to rebel over whether parliament should have more control over any final deal agreed with the EU in Brussels. They planned to vote against a government proposal, which they said did not offer them a "meaningful vote".
At almost the final moment on Tuesday, the two sides agreed to find a compromise and have until 1600 GMT to present it.
A source said a deal had been reached, and that the government would give parliament a vote over its future action if ministers fail to agree a deal by mid-February.
Pro-EU Conservative lawmaker Anna Soubry tweeted: "Deal or no deal, parliament will have a meaningful vote and to be clear there will be no hard #Brexit when the EUWithdrawal Bill is passed."