The Chancellor told Bloomberg that Mrs May did not have “any intention” of leaving before the first stage of the Brexit process is complete.
The comments come after the Prime Minister was handed a potential six-month Brexit delay by EU leaders, taking Britain’s exit date to 31 October.
Mr Hammond said: “The Prime Minister has said that she will leave once she has done the deal and taken us out of the European Union.
“But, as far as I know, she doesn’t have any intention of leaving until that deal is done.
“So, she is a person with a strong sense of duty. She feels that she has got a duty, and an obligation to the British people to deliver Brexit and she will certainly want to make good on that obligation.”
Mrs May told MPs last month that she was not prepared to delay Brexit past 30 June “as Prime Minister” and also vowed to step aside once the first phase of talks with the EU had been completed.
But she has faced anger from some Conservative MPs – as well as a direct Commons call to resign – since being given the potential six-month delay.
The Prime Minister has said she still hopes to get a Brexit deal passed by 22 May to avoid the UK taking part in elections to the European Parliament, an exit date that could also pave the way for a Conservative leadership contest over the summer.
Mr Hammond acknowledged that potential replacements for the Prime Minister were already making open pitches for the top job.
He told Bloomberg: “Let’s be honest, we have already got people jockeying for position to succeed her, but that’s just one of those things.”US serviceman kills woman then himself in Japan