The Portuguese is under increasing pressure to steer the club in the right direction this season after defeat to Brighton last week.
The Red Devils have three points from their opening two Premier League games, and Mourinho’s mood is at an all-time low.
Mourinho is reportedly at war with United’s Chief Executive Ed Woodward over the lack of transfer activity this summer.
The Mirror, UK, reports that even though there are no plans to axe Mourinho now, ex-Real boss Zidane is United’s first choice should the situation with Mourinho continue to deteriorate.
The Frenchman is currently out of job after the Frenchman decided to exit Real just days after winning his third Champions League in a row with the Los Blancos.
The 46-year-old is also thought to be keen on the prospect of managing United and would expect to be contacted should Mourinho exit.
It could cost United £50million to dismiss Mourinho, who signed a new long-term deal until 2020 at the start of the year.
United are back in action on Monday night as the Red Devils take on Tottenham at Old Trafford.
“I think nobody is happy, obviously,” Mourinho told MUTV this week.
“But I have enough experience to know that in football you cannot look back for good results, for bad results and you have always to look to the next one. That’s our life.