Mr Watson, who was elected as Labour’s second in command in 2015, said his former close friend and now general secretary of Unite the Union could “take me out” if he wished.
Relations between the two men, who were briefly flatmates, have been fractious ever since the attempt by Labour MPs to remove Mr Corbyn as the leader of the party in the summer of 2016.
While Mr McCluskey is one of the Labour leader’s closest allies and union backers, Mr Watson told Mr Corbyn he had lost the support of the party following the vote of no confidence in his leadership.
Speaking to the BBC’s Nick Robinson on the Political Thinking podcast, the shadow culture secretary insisted he will not be “bullied”.
Asked about his relationship with Mr McCluskey, he replied: “It is very difficult that, because we were friends socially as well as understood each other politically.
“Sadly, we fell out over that week when Jeremy went into the second leadership election, and I’ve not spoken to him since that week.”
He continued: “I felt very difficult there, because Unite funded my campaign, they didn’t nominate me, and I think he felt that I in some way was obligated to him personally then. And my obligation was to the Labour Party.
“You may severely criticise me for taking the wrong position, and that’s fair, but I’m not going to be bullied by Len McCluskey.”
Asked whether he thought Mr McCluskey was “coming for him”, Mr Watson replied: “Yes, he is coming for me. They’re upping their delegates and all of that.
“What will be, will be. He’s powerful enough, if he wants to take me out as deputy leader, he probably could, but that’s up to him.
“I’m just going to get on and try to bring everyone back together and do what I can as best I can.”
Mr Watson, who was elected deputy leader at the same time as Mr Corbyn took the top job in 2015, said he felt “more chilled out” after losing more than four stone in weight over a year.
“I do genuinely feel a lot calmer, a lot more in equilibrium, so I guess I am a bit more chilled out,” he said.
“This isn’t political, in fact there are the occasional days where I feel like maybe I’m too chilled out for the circumstances I find myself in.
“It adds to resilience and patience, and right now, being deputy leader of the Labour party, those are two qualities I think are quite useful to me.
“The best bit about it for me is that it’s lifted a brain fog that I didn’t know was there. I feel like my mental acuity has improved, almost like my IQ has improved. I feel much sharper.”
Unite declined to comment on Mr Watson’s remarks.