Mourinho and Wenger have clashed on numerous occasions over the past 12 years, with the former Chelsea boss once describing his Arsenal counterpart as a "specialist in failure".
Morgan has made no secret of his desire to see Wenger step down from his role as Arsenal boss in recent years, and he recounted a meeting with Mourinho in Harrods department store during which the United boss reportedly laughed at the Gunners' current plight.
Writing in his column for the Daily Mail, Morgan said: "'I feel so sorry for you Arsenal fans,' he chuckled, not looking remotely sorry.
"'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.'
"'How the hell is Arsene Wenger still in his job?'" I asked. 'No idea,' Mourinho smirked, 'but I hope he stays in it for a very long time..."'
Manchester United currently sit top of the Premier League table, whereas Arsenal are in the bottom half after four games.