Unite is the Labour Party's single biggest donor, providing the party with millions in funding every year.
But there is anger in the union about Labour's direction under Sir Keir Starmer with a source saying he and his inner team were "just not listening".
Sir Keir said he enjoyed "strong relations" with Unite.
The party and the union would "continue campaigning side-by-side and shoulder-to-shoulder" on "important" issues facing workers, he added.
Unite general secretary Len McCluskey was a major ally of the former Labour leader, Jeremy Corbyn, and is a stalwart of the party's Left. He is due to stand down as general secretary in 2022.
Ahead of the meeting of Unite's executive, he told Newsnight another cut in funding might happen if the party changed course too drastically under its new leader.
He said: "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 stand for,' then my activists will ask me, 'Why are we giving so much money'?"
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