According to David Anderson in the Mirror, United are sticking with Mourinho for now despite the Red Devils' poor start to the 2018-19 season, but Zidane is "waiting for the call" and is "very interested" in the Old Trafford job.
Zidane is unattached having stepped down as Real manager back in May.
During his two-and-a-half-year spell in charge of Los Blancos he was hugely successful as the team won three UEFA Champions Leagues in a row, as well as the 2016-17 La Liga title.
Remarkably, the Real job was his first senior management role.
United are already six points off the pace in the Premier League after losing two of their first three matches in the 2018-19 campaign.
A 3-2 defeat at Brighton & Hove Albion was followed on Monday by a 3-0 home loss to Tottenham Hotspur, and Mourinho is now under serious pressure.
If United fail to beat winless Burnley on Sunday the Portuguese's position will become even more precarious despite him having led United to a second place finish in the Premier League last term.
The Old Trafford job would be a test for Zidane. His success at Real was exceptional, but he already knew the setup at the club having been a player there and the reserve team coach.
At United he would enter a club still struggling to re-find their former glory in the post-Sir Alex Ferguson era.
Should Mourinho fail to turn United's fortunes around and be sacked he would be the third manager in succession after David Moyes and Louis van Gaal to not meet expectations at Old Trafford.
While Zidane is far from the most experienced manager around, he would be unlikely to buckle under the pressure at United given how much he achieved in the fierce environment at the Santiago Bernabeu.