"I'm not sure there's a majority in parliament in support for a second referendum, but it's a perfectly coherent proposition," he told Sky News on Sunday.
"It's a coherent proposition and it deserves to be considered," he added, Press TV reported.
Prime Minister May has repeatedly said she is opposed to another referendum, but Hammond now becomes the first minister in her Cabinet to support the second vote.
Hammond’s comments come as the Conservative government finds it increasingly difficult to engineer a smooth withdrawal from the EU.
Opposition Labour Party has already announced that it will push for a second Brexit referendum if its demands are not met in the parliament.
According to recent surveys, a majority of the British public favor the second Brexit referendum.
On June 23, 2016, Britons voted, with a slight majority, for their country to leave the EU.
However, the vote proved to be very divisive with many still urging the government to consider a second referendum that could allow people to vote for Britain to abandon Brexit.
Meanwhile, a number of May's top ministers are reportedly set to topple her within the next few weeks due to her inability to get parliamentary support for a Brexit agreement with the EU days before the deadline to leave the bloc.
The Sunday Times reported that at least 11 unidentified senior cabinet ministers had agreed that the embattled premier should stand down because she had turned into a toxic figure with a judgment that had "gone haywire."
The UK was supposed to secure an exit agreement with the EU by March 29 but the deadline was delayed until April 12 after the prime minister asked Brussels for more time on Thursday.
By then, May should either strike a deal with the EU or proceed with a no deal Brexit, an option that lawmakers have already voted against.