Senior conservative returnee Sir Graham Brady told the BBC he could accept the postponement of Breitsyth – as long as the deal is already agreed.
He said the short delay on the March 29 exit date would be acceptable if needed to bring legislation through parliament.
The government says its position has not changed on the date, but Foreign Secretary Jeremy Hunt has suggested "extra time" may be needed.
Lawmakers rejected a request to postpone Brexit if no agreement was reached by February 26.
That amendment, from Labor MP Yvette Cooper, will postpone the departure date on March 29 for several months but was voted 321 to 298 on Tuesday.
But Sir Graham, chairman of the 1922 conservative influential committee, told Nick Robinson's podcast about political thinking, Cooper's amendment "would be deeply counterproductive, as it moves away from the decision."
Delaying the decision will only lead to greater uncertainty, he said.
"I will just face a delay if we already have a contract agreed, it's just a matter of doing the necessary work to implement it," said Sir Graham.
"Once we reach an agreement and know the conditions for which we are leaving, if we decide that we need two more weeks in order to complete the necessary legislation through the Parliament, I do not think that someone will be too busy to do so because we will make a decision."
The UK is due to leave the European Union at 2300 hours on March 29, but MPs overwhelmingly rejected the withdrawal agreement that the government negotiated with the EU.
On Tuesday, they voted for the prime minister to seek "alternative arrangements" for the controversial Irish draft proposal, which is opposed by many conservative lawmakers and the Party of the Democratic Unionist Party.
Support is an insurance policy to prevent the return of checks on goods and people along the Northern Ireland border if no agreement is reached on time. It will effectively keep the UK inside the EU customs union, but with Northern Ireland also complies with some rules of the single market.
Its critics say a different status for Northern Ireland could jeopardize the existence of the UK and fear that congestion could become enduring.
But the EU's negotiator, Brechitis, Michel Barnier, said on Wednesday that resistance is a "part and parcel" of the withdrawal agreement and will not be negotiated.
Earlier on Thursday, Mr Hunt said it may take "extra time" to finalize Brescht's legislation and the possible delay in Britain's departure from the EU depends on the progress achieved in the coming weeks.
BBC political editor Laura Cuesensberg said there was a "growing speed" about the potential delay and the potential extension of Article 50 – the mechanism by which the UK leaves the EU.
But the official spokesman for the prime minister said the government remains committed to leaving the EU on March 29th.
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Parliament was due to end on Thursday, February 14th and return to Monday, February 25th, but it has now been canceled.
"The fact that does not get weird shows that we are taking all the steps we can take to make sure that March 29 is our way out," the spokesman said.
"The Prime Minister's position on this is unchanged – we will go to 29th place."
Downing Street also discussed the possibility for parliament to sit for additional hours in the run to Brexit, a spokesman said.
Labor leader Jeremy Corbin accused the government of taking off the watch on Brexit.
He said: "It may be that it will have to be an extension in order to reach an agreement, because we can not leave the EU on March 29 without a deal.
"The demolition would mean transportation problems, drug supply problems, supply problems in the food industry that only makes time deliveries – and it's simply not acceptable.
"This government has two and a half years to negotiate and failed to do so."
Meanwhile, Labor MP John Mans said a group of 10 lawmakers from his party met the prime minister two weeks ago to ask for "a substantial amount of money" for poorer areas, so we can actually go ahead as we leave EU ".
When asked about an article from the Times that said Ms. Mai was preparing to encourage MPs to vote for her handling of money for constituencies, Mr Mann said he had already voted for the deal, "so I can not be bribed. "
"There are no expectations, this is not a transaction policy. We are asking for money for areas that in the past did not have a fair share," he said.
Several conservative lawmakers were noticed to attend the Downing Street meetings, including former Minister Brexit Steve Baker, Ian Duncan Smith, a close ally of Ms. May Damian Green and Nicky Morgan.
Ms Morgan, a former education secretary, said she was there to discuss a plan known as the "Malthus Compromise".
The project also includes expanding the transition period for one year and protecting the rights of EU citizens, rather than using the background.
Union officials also met with government officials in the Cabinet of the Cabinet to discuss the Brexit plan of Ms. May
However, a spokeswoman for the trade union trade union congress said the prime minister's deal came "nowhere near" in order to offer protective measures to working people.