The TV presenter, 57, said he had a “pretty fractious” interview with Mr Trump for his new programme on TalkTV, launching next week, as the pair clashed over whether the last US election was rigged.
A promotional video released on Sunday for the special showed Morgan and Mr Trump discussing the Ukraine crisis, with the former president explaining how he would have dealt with the conflict.
Mr Trump said: “Putin uses the ‘N word’. I call it the ‘N word’. He uses the ‘N word’, the nuclear word all the time. That’s a no-no, you’re not supposed to do that. He uses it on a daily basis.
“We have better weapons, we have the greatest submarine power in history.
“I would say, we have far more than you do. We are far, far more powerful than you and you can’t use that word ever again.
“You cannot use the nuclear word ever again.”
Speaking on BBC’s Sunday Morning about the interview, Morgan said he “doesn’t know” if Mr Trump’s approach to the crisis would have worked but that he would have handled it “certainly differently”.
He said: “It is an interesting question, if he was still the US president given his particular way of dealing with dictators like Kim Jong-un of North Korea, and with traditional American enemies like Vladimir Putin, would Putin have actually gone into Ukraine.
“He says not and he has a real problem with how America in particular is dealing with the Ukraine invasion.
“I don’t know, but what hasn’t worked is dealing with this in a conventional manner.
“I have had a feeling from the start of this that we are just showing Putin weakness in the west, we are not engaging with him, and constantly the American president, the German chancellor, going out of their way to say we don’t want to trigger World War III, we don’t want to do anything to upset him.
“This genocidal monster is raising Ukraine to the floor, he’s bombing maternity hospitals, he’s incinerating Holocaust survivors, what is our moral red line?
“If it was a Nato country we would feel apparently a moral duty to engage with him, I don’t see there is any moral distinction frankly other than that they don’t happen to be at this moment in Nato.”
The 75-minute interview, which took place at Mr Trump’s Mar-a-Lago resort in Palm Beach, Florida, will be screened on TalkTV on Monday at 8pm.