The manager has been out of work since leaving Chelsea, but is expected to take charge at Manchester United.
The Portuguese manager is currently out of work, having been sacked by Chelsea in December following a disastrous defence of their Premier League title.
He is yet to agree a deal with another club, although rumours are abound that he could replace Louis Van Gaal at Manchester United.
With Wenger currently under increasing pressure at the Emirates though, Wright has admitted he would not be against Mourinho replacing him in the role.
“Arsenal fans would be up in arms,” he told BT Sport.
“But, I love Jose. If he went to Arsenal, it wouldn’t be something that I would against. I can’t see it ever happening though.”
Given his association with Chelsea, bringing in Jose Mourinho as manager would certainly be a surprising one from Arsenal were it to happen.
However, they will need an elite level manager to replace Wenger when he finally leaves, and there is no denying that the Portuguese boss is in that category.
He has won league titles and Champions Leagues at several clubs, and on that basis alone would not be the worst man the Gunners hierarchy could bring in as Wenger’s replacement.