Mr Osborne, who quit as an MP to become the editor of the Evening Standard, reportedly made the claim to several workers at the newspaper.
The profile in Esquire highlighted the way Mr Osborne had used his editorship of the Evening Standard to criticise Mrs May’s leadership.
The Prime Minister sacked Mr Osborne when she took over at Number 10 and he quit as an MP after the surprise announcement of his move into journalism.
The Esquire profile said: “According to one staffer at the newspaper, Osborne has told more than one person that he will not rest until she ‘is chopped up in bags in my freezer’.”
Tory MP Nadine Dorries said the reported comment was an “insight into the way his mind works”, while Mrs May’s former aide Nick Timothy also took a swipe at the former cabinet minister.
Ms Dorries, who previously clashed with Mr Osborne and his ally David Cameron, said the piece was “a brief insight into how his mind works – and always has”.
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Mr Timothy highlighted a quote in the piece from a former aide saying Mr Osborne “doesn’t want people to think he’s an a*******, because he’s not an a*******”.
Mrs May’s former joint chief of staff added: “Not sure why he worries people think he’s an a*******.”
Asked for the Prime Minister’s reaction to the Esquire piece, her official spokesman said: “The contents of the former Chancellor’s freezer are probably not a matter for me.”
Mr Osborne has used the Evening Standard’s editorial paged to repeatedly attack Mrs May, labelling her a “dead woman walking” after she lost her majority in June’s election.
Despite this, Mr Osborne told Esquire that was not trying to settle any personal grudges.
He said: “Most newspapers are very partisan. I’m sticking it to the Corbynista left and the hard-Brexit right.
He added: “I’m paid to produce a paper that has attitude and gives voice to people whose voices are not being heard, and I don’t really give a damn if some are offended by that.”