The union, which is Labour’s biggest financial donor, was understood to be reducing affiliation by about 10 per cent after a vote of its executive on Tuesday.
Mr McCluskey, an ally of Sir Keir’s predecessor Jeremy Corbyn, warned Unite’s multi-million pound funding could be cut if the new leader undertakes a too drastic change of course.
Ahead of the vote, Mr McCluskey told BBC Newsnight: “I have no doubt if things start to move in different directions and ordinary working people start saying, well, I’m not sure what Labour stands for.
“But I don’t see at the moment any dramatic move to disaffiliate from the Labour Party. The Labour Party is our party.”
However, he was particularly critical of Labour’s payout to whistleblowers over the party’s handling of anti-Semitism under Mr Corbyn.
“I think funding arrangements is undoubtedly an issue that may come up,” Mr McCluskey added.
There is some frustration on the Labour left that Sir Keir ran for the leadership on the party’s left but has quickly moved to the centre since winning the contest in April.