Mourinho got off to a slow start upon taking the reins at Old Trafford and appeared doomed to suffer through the struggles of his precedessors David Moyes and Louis van Gaal in filling the huge void left by Ferguson.
But United have been much improved in recent months and have not suffered a domestic defeat since their 4-0 humbling at the hands of Chelsea in October.
Though a number of draws have held them back over the course of the campaign as a whole, the Red Devils won nine games in a row in all competitions either side of the New Year and now sit two points behind fourth-placed Manchester City in the Premier League.
Ferguson believes the revival can be credited to Mourinho gradually imposing his own values and identity on the team.
“The team is mirroring its manager,” the 75-year-old told BBC Sport. “It’s playing with great energy, determination, will to win – which I think is really important.
“If they hadn’t had all these draws I think they would be there challenging Chelsea. That’s the unfortunate part and he’s going to have to live with that, but I think he’ll be inspired by the progress of the team.”