Zidane stepped down from his position a few months back after guiding Los Blancos to three back-to-back Champions League titles.
The 46-year-old is now out of work since resigning as manager of Los Blancos in May 2018, just five days after winning his third consecutive Champions League trophy.
The Portuguese left his first spell at Chelsea shortly after starting his third year at the club, before a hugely successful two-year stay at Inter Milan preceded a three-year stint at Real Madrid.
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.
United finished 19 points behind runaway winners Manchester City last term and Mourinho has been unapologetic in voicing his dissatisfaction with the lack of sufficient reinforcements this summer.
Ben Stokes found not guilty of affray over street fight
He and his teammates were out celebrating England's win against the West Indies when a fight broke out and led to Stokes' arrest. But the jury returned a verdict of not guilty against the England cricketer and also cleared Ali of the same charge.
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.
United's executive vice-chairman Ed Woodward was unable to strike a deal for either Tottenham's Toby Alderweireld or Bayern Munich's Jerome Boateng who were both wanted by Mourinho.
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The Frenchman has now won the last three Champions League titles in a remarkable run, whilst he has also won one La Liga title, but he chose to move on this past summer.
"What he and [Lionel] Messi have done is just different, I don't think you'll see it again".