Opposition Leader Malcolm Turnbull says former treasurer Peter Costello has recently told him that he is not interested in the Liberal leadership.

It has been a difficult week for the Coalition, with a dispute about the circumstances of an offer to Mr Costello to become shadow treasurer, a gaffe by frontbencher Tony Abbott, and the sacking of frontbencher Cory Bernardi.

"The [Costello] issue is closed," Mr Turnbull told Fairfax Radio this morning.

"I don't want to go into private conversations.

"Peter and I have discussed it and we agreed that what I would say, and the position would be literally, that he has made it clear that he is not interested in a frontbench or leadership [position].

"Peter has made it very clear that he is not interested in either a frontbench or leadership role."

Mr Costello has repeatedly refused to spell out his political future and whether he has aspirations for the Opposition leader's role.