The Red Devils boss is fighting to save his job at Old Trafford after a summer of upheaval at the club.
Mourinho could face the axe should Manchester United fail to turn their form around against Tottenham and Burnley in the coming weeks.
And Zidane reportedly believes he will take over from the Portuguese coach should he lose his job in the near future.
According to the Daily Mail, the former Real Madrid boss has told close friends that he is the leading candidate for the United role and would be very interested in replacing Mourinho.
Last season’s Premier League runners-up have publicly backed the former Chelsea boss this week, with a source telling the BBC: “Why would we discuss him when there is no job available?”
But the Mail report United know they must have a plan in place should Mourinho be unable to turn the tide in the next few weeks.
Zidane resigned from Madrid earlier in the summer after a successful two-year tenure at the Bernabeu.
The former Juventus star won three consecutive Champions League titles after replacing Rafael Benitez in 2016.
Zidane was touted as a potential candidate for the Qatar national team job, where the 2022 World Cup hosts were prepared to offer the former midfielder £44m-a-year to take over at the helm.
However, he appears to be waiting for the right job at club level before returning to management.
As for United, Mourinho will be hoping his side can put their 3-2 defeat to Brighton behind them when they take on Tottenham on Monday.
And new signing Fred has moved to publicly back the manager ahead of the clash.
“I’m really happy to be working with Jose Mourinho he’s a great person and he’s always keen to communicate with the squad and help people to be communicative regarding what they’re to do on the pitch,” he told Sky Sports.
“I’m really happy to be working with him and I hope that I’ll be working for him for a while to come.”
United welcome Spurs to Old Trafford on Monday evening.