Mourinho has come under increasing scrutiny during pre-season after cutting a rather miserable figure at times. He has been prickly throughout United's summer tour, complaining about everything from performances, a depleted squad, players, travel commitments and transfers.
The Portuguese has never spent more than three seasons in any job in his managerial career to date. As his third year at United kicks off, some now believe it will be his last.
And The Sun claims to have been informed by Old Trafford sources that Zidane, who is currently out of work after resigning from his position at Real in June, would be the 'first call' that United would make in the event that Mourinho is no longer manager.
The newspaper suggests that some United players are convinced the 2018/19 season will be his last at the club, despite holding a contract until 2020.
Zidane was a serial winner during a short two-and-a-half year spell at Real, winning the Champions League an historic three times and also masterminding only the club's second league title in a decade when he steered the team to La Liga glory in 2016/17.
The real challenge for the Frenchman, who was a three-time FIFA World Player of the Year before hanging up his boots, is to prove that his success in Madrid was the result of his expert coaching and guidance rather than born out of circumstance because of the quality of the squad.
United wrapped up their turbulent pre-season tour with a 2-1 win over Real on Tuesday night.