On whether he had received an invite for the May 19 wedding, Donald Trump told British journalist Piers Morgan in Morgan, "Not that I know of".
He said Prince Harry and Ms Markle looked "like a lovely couple".
American actress Meghan Markle was a Hillary Clinton supporter in the 2016 US election, and has referred to Mr Trump as "divisive" and a "misogynist", BBC reported.
Donald Trump said he had been offered two visits to the UK this year by British Prime Minister Theresa May -- a working visit in the summer and a state visit in the autumn, Piers Morgan tweeted.
But Downing Street has not confirmed the claim.
During the interview, Mr Trump also declared that he is not a feminist. "No, I wouldn't say I'm a feminist. I mean, I think that would be, maybe, going too far. I'm for women, I'm for men, I'm for everyone," Mr Morgan tweeted, quoting the US President.
On his social media habit, Donald Trump said he would often tweet "perhaps sometimes in bed, and perhaps sometimes at breakfast, or lunch, or whatever", but added that he would also delegate some of his tweeting to someone else.
The Piers Morgan Interview will be broadcast on Sunday on ITV.