"Both sides want a Brexit deal that supports ongoing friendship between UK/EU/France so patience and goodwill on backstop now the critical ingredient", he tweeted.
British lawmakers overwhelmingly rejected May's withdrawal deal last month, with the major sticking point being the Irish "backstop" - an insurance policy to prevent the return of a hard border between the British province of Northern Ireland and the Irish Republic.
Last week, Labour leader Jeremy Corbyn set out five conditions for his party's backing of the prime minister's withdrawal agreement.
On Wednesday, Theresa May played down the possibility of a delay and told MPs in parliament they should not rely on "what someone said to someone else as overheard by someone else, in a bar".
Corbyn also accused the Prime Minister of "recklessly running down the clock" so that MPs would have to vote for her Brexit deal.
For his part, Bank of England chief Mark Carney warned that leaving the European Union without a transition deal "would be an economic shock for this country", and said Brexit was an "acid test" of the globalised economy. "We now all need to hold our nerve to get the changes this House requires and deliver Brexit on time".
The EU's Brexit negotiator, Michel Barnier, said on Monday the bloc would agree to tweak the political declaration on post-Brexit EU-UK ties that forms part of the exit package, to reflect a plan for a closer future relationship that could remove the need for the backstop.
Mrs May sought to buy time, telling lawmakers they would get another chance to alter her course on February 27 if she had not secured changes to the Brexit deal by then.
According to the UK-based media outlet, senior Tory and Labour lawmakers allied to set a new, legally-binding deadline of mid-March for any EuropeanUnion agreement to be ratified.
The measure, known as the backstop, is a safeguard mechanism that would keep the United Kingdom in a customs union with the EU and removes the need for checks along the border, until a permanent new trading relationship is in place. But any such move would cost May the support of a big chunk of her Conservative Party.
Earlier in the day, the Leader of the House of Commons Andrea Leadsom refused to rule out delaying the British parliamentary vote until as late as the week prior to Brexit, following an European Union summit scheduled for March 21. The prime minister, if she went through the lobbies for this tomorrow night, would be voting against the guarantees she has given in the Commons for months [that no-deal remains an option].
May's office declined to comment Tuesday on what it called "alleged remarks", and said its focus was on seeking changes to her deal that Parliament would accept. "It's not possible to predict the future", she told the BBC.
The Brexit uncertainty is beginning to be felt across the economy.
On Tuesday representatives from 32 food industry groups said in a letter to Rural Affairs Minister Michael Gove that the industry was facing a crisis and companies were "now totally focused on working to mitigate the catastrophic impact of a no-deal Brexit". Figures released Monday showed that Britain's economy slowed a year ago to its joint-slowest annual rate since 2009, with business investment declining for four straight quarters.