The 46-year-old is currently 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.
Zidane also won La Liga with Madrid in 2017, as well as two Club World Cup trophies during his two-and-a-half years as first-team manager at the Santiago Bernabeu.
According to L’Equipe, Zidane is already considering his next role and has his sights set on the Premier League.
The report claims that the World Cup-winning midfielder is especially keen on managing Manchester United.
Mourinho is under increased pressure to deliver success to United after failing to win a trophy at Old Trafford last season.
Despite finishing 19 points behind Manchester City, Mourinho is adamant that last season’s second-placed finish in the Premier League should be considered as one of his ‘biggest achievements’.
Mourinho, however, has been at odds with United’s hierarchy this summer, primarily over their refusal to sign an experienced central defender before the transfer window closed last Thursday.
Tottenham’s Toby Alderweireld and Bayern Munich’s Jerome Boateng were both wanted by Mourinho, but United’s executive vice-chairman Ed Woodward was unable to strike a deal for either player.
Mourinho warned United’s board that the club face a ‘difficult season’ if the squad was not improved.
And Mourinho also disagreed with Woodward over the future of Anthony Martial, with the United manager happy for the French forward to be sold.
Last month, reports claimed that United have Zidane on their shortlist of candidates to replace Mourinho if the 55-year-old leaves at the end of the season.