Ferguson, 76, collapsed in his home on Saturday and underwent emergency surgery. He is currently in Salford Royal Hospital.
Asked at a news conference Wednesday how the former United boss was, Mourinho said: “We are confident.”
He added: “His family asked for privacy and that is what I am going to respect.
“But [as a club] we are positive. We are very, very positive.”
The Portuguese’s comments were the first said publicly by anyone directly connected with the club since Manchester United’s initial statement Saturday which said that surgery had “gone very well.”
There have been a deluge of messages on social media wishing the Scot well, with his former star players Cristiano Ronaldo and David Beckham among those wishing their former boss a quick recovery.
The Glasgow-born Ferguson retired in 2013 as the most successful manager in the history of the English Premier League.
In nearly 27 years in charge of United, he won more than 30 trophies — including 13 league titles, two Champions League trophies and five FA Cups.
He was voted manager of the season 11 times, after his teams won 528 times in 810 matches.
Before moving to United in 1986, he also led Aberdeen to three Scottish titles, four Scottish cups, one League Cup and one European Cup Winners’ Cup.