Amorim has struggled to make an impact since joining United from Sporting Lisbon last November but his compatriot thinks that he can turn things around at Old Trafford if he is given the chance.
Mourinho told Portuguese TV channel Canal 11: "What happened to Ruben, from being the manager of the worst Manchester United in Premier League history to having continuity and confidence to continue and be Ruben Amorim, is a sign that a lot needs to change.
"With that stability... we all agree that he's a manager, with great potential and personality. I think he has incredible potential to do great work."
United have struggled since Sir Jim Ratcliffe's INEOS group took control of football operations last year and Mourinho has questioned whether the ownership has the requisite experience of the beautiful game.
The former Red Devils boss said: "Today, I think that with the change in ownership at the club, with an owner who doesn't have much experience in football but rather in sport."
Mourinho believes that United's decline can be traced back to the departures of legendary manager Sir Alex Ferguson and former chief executive David Gill in 2013 – although he believes that his team "legally" won the Premier League title in 2018 as they finished second behind a Manchester City team who have been charged with financial fair play breaches.
He said: "There's a critical moment at that club, not only with Sir Alex's departure, but also with David Gill's. David Moyes came in, but when my Netflix documentary comes out, the story will be told.
"I'll arrive later, and when I arrive, I'll arrive at the club still going through that period. We won several things, we finished second in the league. I still say I don't understand clubs that are punished with financial fair play and pay (in cash)."
Mourinho added: "I think they should pay points. Manchester City was punished, and legally, we should have won the league. But it wasn't enough for me to have stability, continuity."