Morgan, writing in his Daily Mail column, says he ran into Mourinho in upmarket department store, Harrods in London, near where his family is based, after the Gunners were battered 4-0 by Liverpool.
The two men had a 20-minute chat about football, in which Mourinho threw some brutal jabs at the Gunners and their manager, Arsene Wenger.
Morgan wrote: “I feel so sorry for you Arsenal fans,” he chuckled, not looking remotely sorry.
He quoted Mourinho saying: “I have some very good friends who love Arsenal like you do and they are just as depressed as you about the club.
“They suffer so badly, it is a terrible thing to observe. Mourinho then burst out laughing. “Terrible… hahahahaha.”
Morgan says he asked: “How the hell is Arsene Wenger still in his job?”
Mourinho’s response, as reported by Morgan, is brutal: “No idea,” Mourinho smirked. “But I hope he stays in it for a very long time…”‘
The pair took a picture, which Morgan uploaded on his Instagram page.