Reports says Sir Alex will retire at the end of next season.
A United insider told News of the World: “Mourinho is the name being mentioned most behind the scenes among the top brass. He has the kind of personality and successful record needed to take on the enormous task of succeeding Sir Alex.
“He became very close to Fergie during his time at Chelsea and there is a mutual respect. The Glazers will rely heavily on Sir Alex in the naming of his replacement.
“Fabio Capello would be another contender because Fergie rates him highly too but the Italian has already stated the England job will be his last in football.”
A highly-placed Chelsea source said: “Jose always made his love of United very clear, in fact he was obsessed with them and talked about being in charge of the biggest club in the world.
“He wanted to test himself in Italy when he left the Bridge, but it was obvious to most people he wanted to come back here with United to haunt us.”