Asked if he would jump before he was pushed if Johnson takes the Tory crown in two weeks' time, Hammond told ITV's Peston: "My expectation is that I will not be serving in the next administration".
May, who is now serving as caretaker Prime Minister during the course of a leadership contest between United Kingdom foreign secretary Jeremy Hunt and former foreign secretary Boris Johnson, was forced to announce her resignation amid mounting rebellion within her own Cabinet over Brexit at the end of May.
Asked by Sky News how many jobs would be lost in no-deal scenario, Clark said: "It's many thousands of jobs".
In an interview on Friday Clark warned if the United Kingdom quits the European Union with a no-deal Brexit the disruption would lead to thousands of jobs disappearing.
"I think, somehow, Alex, much as I love the USA, much as it would be a dream job for me in many ways, I'm afraid I've got to stick around in case they drop the ball again".
A spokeswoman for Mrs May told a Westminster briefing: "The Prime Minister has always been clear that leaving without a deal would be disruptive".
The polemical candidate is now trying to shut down the parliament, though some have warned him that such a move, which would force a no-deal Brexit, would tear down the government and even some may take legal actions against him.
Mr Hunt, however, warned that "the big risk" facing the Conservative Party was ending up with an election and no departure "if we approach Brexit in a headstrong way".
Alongside David Gauke and Greg Clark, Rudd previously attempted to force Theresa May torule out no-deal ahead of the original Brexit deadline of March 29.
The outgoing PM, who will be exiting Downing Street to make way for Hunt or Johnson by July 23, said she felt a "mixture of pride and disappointment" and that despite having to go earlier than she wanted, she had been the "right person" for the job and was "immensely proud" of what she had accomplished.