The former Chelsea boss has been heavily linked with Louis van Gaal’s position since he was sacked by the defending Premier League champions in December.
Mourinho is the favourite to take over at Old Trafford in the summer, although Ryan Giggs remains a contender to fill Van Gaal’s shoes.
Arsene Wenger, meanwhile, is facing an uncertain future after some Gunners supporters turned on the Frenchman following their FA Cup and Champions League exits.
The long-serving Arsenal manager has a long-running fued with Mourinho, who he has never beaten in the Premier League.
But outspoken Arsenal supporters Morgan believes Mourinho is the right man to succeed Wenger at the end of the season if the Gunners manager leaves the notrth London club.
If Mourinho to Utd is not a done deal, as papers suggest, Arsenal should break the bank for him.
— Piers Morgan (@piersmorgan) March 21, 2016
Arsenal were 2-0 winners against Everton at Goodison Park on Saturday to end a three-game winless run in the Premier League.
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