Speaking to the BBC on Sunday, business minister Greg Clark - who served under Osborne - said Carney had been "a brilliant appointment".
Saturday's edition of the Times - which is editorially separate from its Sunday sibling - had previously reported Carney's motivation for leaving in 2018 was more personal.
"Senior City figures who know the governor said they believed it was more likely than not that he would choose to return to Canada in 2018, adding that his family's feelings were a concern," the Times had said.
"Suggestions he could leave before 2018 were firmly rejected," it added, saying an announcement could come at Thursday's news conference or a future appearance before the committee of lawmakers which monitors the central bank.
The BoE declined to comment on the Times article and referred to Carney's previous public statements on the topic.
Last week, Carney said his decision whether to stay would be based on personal rather than political considerations, and he would need to find some time to make up his mind.
The report that Carney was unhappy with May's office was based on information from two senior figures who had known Carney since he moved to Britain in 2013, the Sunday Times said.
"I don't think he's been overly impressed by the professionalism of No. 10," the Sunday Times quoted someone described as a friend of Carney as saying about May's office.
The Sunday Times said government officials did not expect Carney to announce his departure as soon as Thursday, and said friends of Carney expected him to stay in his job until 2018.