The Good Morning Britain (GMB) host had the first international interview with Mr Trump as president at the World Economic Forum in Davos, Switzerland, in January last year.
Morgan, 54, said he was “working on” a follow-up “long-form” interview that he planned to hold inside the White House.
He said: “The last time I saw him was on Air Force One [the aircraft used by the US president] and he said I could come to the White House and do the next one there.
“I imagine the next time you will see me pop up, which I know will bring huge joy to people, especially my journalistic rivals who never get him, is probably at the White House.
“That’s what I am working on.”
Morgan said he expected the interview to “straddle” a host of publications, including GMB, ITV, MailOnline and the Mail on Sunday.
Asked what viewers should expect from their next meeting, Morgan replied: “I think another long-form interview, yes.”
Morgan met President Trump in 2008 when he appeared as a competitor on the celebrity version of The Apprentice in the US, which he went on to win.
The presenter has previously said he is a friend of the president, but last year aired his disagreement with Mr Trump’s ban on immigrants from seven majority Muslim countries.
Morgan attributed exclusive interviews such as those with Mr Trump to the success of GMB, which on Monday saw its highest ratings share ever.
At 6:30am, 33 per cent of viewers were watching GMB while 41 per cent tuned in to BBC One. GMB had an average of 25.3 per cent across a two-and-a-half hour slot.
The ITV daytime show’s ratings are up 10 per cent on the same period last year and the show this year received two Bafta nominations for best news coverage for their piece on knife crime and an interview with Thomas Markle.