The BBC host also took the chance to take a dig at Prime Minister Theresa May after she reshuffled her Cabinet.
Mr Neil said: “And the more astute among you who are not on a permanent balloon on haze over the festive season will have noticed that a loser lick-spittle of the mainstream media has just published a farrago of lies and inventions about me.
“Now, since I’m better with pictures than words, I had to have the wife read it to me: this seemed to give her an inordinate pleasure which somewhat baffled me as did the thick, East European accent.”
Mr Trump became the subject of international scrutiny after journalist Michael Wolff published a book titled “Fire and Fury. Inside the Trump White House” sharing an unflattering account of the President’s first year in office.
Mr Neil used his monologue at the beginning of his weekly stint as This Week host to lay into Mr Trump’s reaction to the book’s publication.
He continued: “The book makes me out to be thicker than Jack Thick McThick the year he won the Thick Man of the Year competition, also claiming I’m a sandwich short of a picnic and two-stairs short of an attic. How is this double shuffling, honeyfuggling, horn swaggler of a journalist in a position to say any of that?
“You know I’m so smart I’m bordering on genius. In fact, strike the word bordering or I will build a wall. Anyway, I called my Britisher friend, Mother Theresa, who is always ready to hold my hand when fake news surrounds me.”
The BBC presenter then took aim at Mrs May for her “baffling” reshuffle, suggesting it had not changed the general outlook of the Cabinet.
He added: “She said not to trust the This Week team who’ve clearly speaking bigly to this loser, loser, loser author whom I’ve never met and to announce an immediate reshuffle of my entire team, including some public sackings.
“To make absolutely no changes whatsoever” ‘That’ll baffle everybody,’ said Mother Theresa. ‘It worked for me,’ she added. And so I did.
“Nobody has a clue what I’m doing, not even me. If that’s no genius I don’t know what is.”
It comes after Mr Trump cancelled his trip to the United Kingdom to inaugurate the new US Embassy building in London after fears it would be unwelcome.
Trump has decided not to attend the event, sending Secretary of State Rex Tillerson in his place, in a major diplomatic snub to the UK.
The move is likely to frustrate Theresa May who insisted just days ago that “he will be coming to this country” during a TV interview.