Zidane left Real Madrid at the end of last season having guided the La Liga giants to three consecutive Champions League titles.
Mourinho is under severe pressure after a disastrous pre-season.
There are concerns that this is the beginning of the end for the Portuguese at Old Trafford.
The Sun, UK, reports that the club officials are in no doubt that Zidane would be top of the list of new managers if Mourinho did leave.
Mourinho has in recent days criticized United’s transfer chiefs for failing to sign the five players he requested at the start of the summer.
The former Chelsea boss also faces a major task to close the gap on Manchester City this season.