Andrea Leadsom has said that the EU may be prepared to grant the UK a "couple of extra weeks" beyond the 29 March deadline to finalise preparations for Brexit.
The Commons leader said that in light of the UK's strong relationship with its "EU friends", the UK could be allowed more time for an approved deal to pass all its parliamentary stages.
But Ms Leadsom accused the EU of being in denial about the unease in the UK over the Northern Ireland backstop.
In a rebuke of Amber Rudd and Philip Hammond, the Commons leader called on the cabinet to rally behind Theresa May and accept that the UK will leave the EU without a deal if MPs reject her deal.
In an interview with BBC Newsnight, Ms Leadsom said she had "grave concerns" about a bill, proposed by Labour MP Yvette Cooper, which could extend Article 50 by nine months.
But she said that the EU could agree to allow the UK to remain in the EU for a few weeks longer than the March deadline. This could happen if a deal has been reached, but more time is needed for parliament to approve its Brexit legislation.
A Downing Street spokesman said: "There is no change to our position. We are not considering an extension to article 50 and are committed to doing whatever it takes to have the statute books ready for when we leave the EU on March 29th this year."
Ms Leadsom, who is in charge of timetabling government business in the Commons, said: "We can get the legislation through and I think we do, in spite of everything, have a very strong relationship with our EU friends and neighbours and I am absolutely certain that if we needed a couple of extra weeks or something then that would be feasible."
In answer to the suggestion that this would amount to an extension of Article 50, which is due to conclude on 29 March, she said: "It doesn't necessarily mean that. I think we would want to think carefully about it. But as things stand I do feel that we can get, with the support of both Houses - the House of Commons and the House of Lords - with goodwill and a determination we can still get the legislation through in good time."
In the interview, Ms Leadsom highlighted tensions when she was asked about cabinet discipline, after the warnings from Ms Rudd and Mr Hammond about the dangers of a no deal Brexit.
"I'm totally aligned to the prime minister," she said. "I believe that is where collective responsibility should lie.
"So number one, the legal default is we leave the EU on 29 March without a deal, unless there is a deal in place. That hasn't changed. That is the prime minister's view and that's my view.
"Of course, it is also very important that we continue to prepare for all eventualities because we do need to make sure that in all circumstances the UK can continue to thrive and do well in a post EU environment.
"I do encourage my colleagues in cabinet to get behind that sentiment and to make sure that we are all on the same page. We are now in the really final days."
Backstop 'a real problem'
Ms Leadsom was highly critical of the the EU for failing to understand the deep unease in the UK over the Northern Ireland backstop.
In the most contentious area of the deal, the UK and the EU have agreed to avoid a hard border between Northern Ireland and Ireland by binding the former closely to EU rules.
This would apply after the transition period if the UK and the EU have failed to negotiate a future relationship by then.
"Keeping the UK in an unlimited, in time terms, backstop that we can't unilaterally exit from under any circumstances is a real problem for many," she said.
"Resolve that and [many Conservative MPs and the DUP] can support the prime minister's deal.
"The EU need to be listening very carefully to that. They are slightly in denial saying that that is not the issue. It very much is the issue.
"So I am hoping the European Commissioners will look very closely at the backstop and think of a way through this, because the legal default is that we leave the EU on 29 March without a deal unless we can agree a deal."
Ms Leadsom was speaking to Newsnight during a visit to Manchester to highlight her work chairing a cross-government group on early years intervention.