Mourinho is under increased pressure to deliver success to United after failing to win a trophy at Old Trafford last season.
The former Real Madrid boss, who surprisingly left his post in Spain just days after winning a third consecutive Champions League, is 7/4 (2.75) with William Hill to be the next man in charge at Old Trafford.
According to the French media outlet L'Equipe, Zidane is already considering his next role and has his sights set on the Premier League.
The 46-year-old is now out of work after he resigned as Real Madrid manager in May just five days after guiding the club to their third consecutive Champions League trophy.
Instead Zidane will instead take a year off to relax following the mental stress he was under at Real Madrid. And according to the bookies, Mourinho is the second favourite at 6/1 to be the first Premier League manager to leave this season.
Pellegrini disappointed with West Ham performance against Liverpool
This isn't necessarily the flawless fit for the electric pace of Liverpool's front three. West Ham were a mess, make no mistake about it.
Former Manchester United winger Ryan Giggs was also among the list, while Antonio Conte, Luis Enrique and Brendan Rodgers, of all people, are also linked.
During pre-season, Mourinho lamented the lack to acquire priority targets which seemingly aroused tension between him and club Chief Executive Ed Woodward. However, should Zidane contact the United hierarchy about becoming their manager, they will need to make a quick decision or risk losing the Frenchman to another Premier League club.
The news may please United fans, and would surely leave Paul Pogba and Anthony Martial feeling optimistic - and not just due to their seemingly frayed relationships with Mourinho.
And Mourinho also disagreed with Woodward over the future of Anthony Martial, with the United manager happy for the French forward to be sold.