Mourinho is under huge pressure win the Premier League this season after failing to win a trophy at Old Trafford last campaign.
Zidane enjoyed an extremely successful spell in charge of Real Madrid, guiding them to three consecutive Champions League triumphs and the La Liga title.
United did win their opening Premier League fixture 2-1 against Leicester City on Friday evening but Mourinho has already made clear his belief he doesn't have the squad to challenge reigning champions Manchester City.
Zidane was heading the Whites from 2016 to 2018, and won nine titles with the Real Madrid.
Many United fans are unhappy with Jose Mourinho's demeanour and style of play, with some looking for him to be replaced in what is - historically - a crucial third season for Mourinho's reign.
Mourinho, however, has been at odds with United's hierarchy this summer over their refusal to sign an experienced central defender before the transfer window got shut last Thursday.
Mourinho is under increased pressure to deliver success to United after failing to win a trophy at Old Trafford last season.
United's executive vice-chairman Ed Woodward was unable to strike a deal for either player Tottenham's Toby Alderweireld and Bayern Munich's Jerome Boateng who were both wanted by Mourinho.
Mourinho is still under contract at Manchester United and will continue as manager for the foreseeable future.
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