Scaramucci said he had spoken to Trump after resigning: "The President told me he knows I have his back, but he has to try to tighten the ship."
He also had a "very polite" conversation with John Kelly, the incoming chief of staff who asked for his resignation.
Scaramucci still has the President's mobile phone number.
According to the Huffington Post, before the New Yorker interview Scaramucci had been irked by false rumours of an affair with Kimberly Guilfoyle,a Fox News host. The two are long-time friends.
That led indirectly to a phone interview with journalist Ryan Lizza of the New Yorker.
Scaramucci told the Huffington Post he thought the conversation was off the record "in spirit".
He said: "The Lizzas and Scaramuccis have been friends for over 50 years. My dad knew his dad from construction, and we were building a personal relationship.
"Most of what I said was humorous and joking. Legally, it may have been on the record, but the spirit of it was off. And he knew that."
Lizza categorically disputes that, saying: "We are not and have never been 'old family friends' though I think our fathers knew each other, so maybe that's what he's talking about.
"But again, that would not be a reason to suppress an explosive on-the-record interview."
This story was originally published by the Daily Telegraph.