Wenger will step down at the end of the season, leading to rampant speculation over who will replace him.
Surprisingly, Liverpool No.2 Zeljko Buvac is the reported frontrunner, having taken an unexpected leave of absence from Anfield.
Mourinho was subsequently asked about the possibility of Faria stepping away from his side to move into the dugout, and the Portuguese has suggested that his childhood friend could thrive if given the responsibility.
"I think so, yes. I don't know (if he wants to be a manager). You ask me if I think it would be a good fit and I say 'yes'," he told reporters.
"And I say it because more than my assistant, he is my friend. If my friend has the possibility one day of a big job I would help him to pack and to carry the bags and to wish him luck.
"So, if one day that is going to happen the first one to be happy would probably be myself because I met him when he was a kid in his university and we were together for 18 years, so he is a big friend, more than an assistant.
"So, if one day the moment arrives, I will be very happy."