Sir Graham Brady said “clarity” on the controversial backstop was more important than the timing of the vote on the Prime Minister’s agreement.
It comes after Mrs May was urged by some Cabinet ministers to postpone the vote, which many of her fellow Conservatives expect she will lose.
Sir Graham, chairman of the backbench 1922 Committee, said he would welcome the vote being deferred if no solution could be found to differences within the party over the Northern Ireland border backstop.
He told BBC Two’s Newsnight: “I think the most important thing is to have clarity about how we might remove ourselves from a backstop … if we were to enter into one in the future.
“It’s having the answer to that question of substance that is most important, not the timing, so if that question can be answered in the course of the next few days then all well and good.
“If it can’t, then I certainly would welcome the vote being deferred until such time as we can answer that question.”
MPs tabled earlier tabled an amendment to the meaningful vote on the deal that would give MPs some control over the controversial backstop, which has been the main sticking point after two years of negotiations
The alteration would mean Parliament will have to approve a decision to trigger the backstop arrangement or extend the transition period beyond December 2020.
It was tabled by Northern Ireland minister Sir Hugo Swire, Richard Graham and Bob Neill, hours after the Prime Minister indicated Parliament would choose between the two options after the UK formally quits the EU.
The move is likely to be seen as a bid to bolster flagging support for Mrs May ahead of a crunch Commons vote on her EU withdrawal deal next Tuesday – a showdown the PM made clear on Thursday morning she would not postpone.
But it remains to be seen whether it goes far enough to win over enough Tory Brexiteers to get the deal through the Commons.
DUP leader Arlene Foster, whose party opposes Mrs May’s deal, warned that the amendment would not be enough, tweeting: “Domestic legislative tinkering won’t cut it.
“The legally binding international Withdrawal Treaty would remain fundamentally flawed as evidenced by the Attorney General’s legal advice.”
The backstop, intended to prevent the return of a hard border in Northern Ireland, is highly controversial as Brexiteer MPs claim it traps the UK into obeying rules set by Brussels without a say over them.
The Government says it aims to conclude a comprehensive trade deal with the EU before a backstop arrangement would be needed.
Under the Withdrawal Agreement, the backstop would be introduced if a trade deal had not been agreed by both sides by the time the transition period ends in December 2020.
However, the transition period could be extended for a maximum of two more years.