But he said that talking about pushing May out was "frankly self-indulgent at this time".
The Chancellor told Sky's Ridge on Sunday programme that replacing Theresa May would not "solve the problem".
Liberal Democrat leader Sir Vince Cable told talkRADIO: "It's the last big chance for the people to get out on the streets and argue for a People's Vote while we still have a good chance of getting there, resolving this terrible problem in that way". And if Saturday's demonstrations are any indication, May is also losing support among voters.
One of Theresa May's most senior cabinet ministers has raised the prospect of a second referendum to break the Brexit deadlock, as speculation over the future of the beleaguered United Kingdom prime minister and her twice-defeated divorce bill reaches fever pitch.
On Saturday, hundreds of thousands of people marched in central London to call for another European Union referendum.
When asked about possible options for Brexit, Mr Hammond said he was not sure there was a majority in parliament for a second referendum but that it was a coherent proposition. EU Council President Donald Tusk on Wednesday agreed to give Britain an extension to its Brexit deadline but only if the British Parliament agrees on a deal next week.
If the vote is not passed, the United Kingdom will have to set out an alternative way forward by April 12, which could mean a much longer delay - with the United Kingdom required to hold elections to the European Parliament - or leaving without a deal at all.
"Whoever is prime minister we will work with them".
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But with her parliamentary allies the Democratic Unionist Party indicating they remain opposed to her plan, that appears unlikely.
The Prime Minister brought back memories of her 2017 Conservative Party Conference speech as she was reduced to a croak as she addressed MPs in the Commons.
"It's looking very hard to bring together a majority for it", Hammond conceded to Sky News.
MPs will be given the chance to seek to take control of the Brexit process from the Government if they back plans for a series of indicative votes when they vote on their favoured Brexit outcomes on Monday night.
A similar move earlier this month failed by just two votes.
Mrs May also faces pressure from groups demanding a second Brexit referendum. A British election could be the outcome of parliament seizing control of the Brexit process if lawmakers back proposals contrary to the pledges the government was elected on, Barclay said.
"If Theresa May struggles to command the respect of Parliament, to command the respect of government, to command the respect of the nation, and to command the respect of Brussels, how on earth is David Lidington - who nobody has heard of - going to command the respect of all four?" he said.
"There is a constitutional collision if parliament is instructing a government to do something that is fundamentally against what it has been elected to do", he told the BBC.