The France international has struggled to hold down a regular starting spot in the Manchester United team since Mourinho took over the reins from Louis van Gaal in May 2016.
Martial moved to the 20-time English champions in a £36m deal from Ligue 1 side AS Monaco in the 2015 summer transfer window.
The 22-year-old scored on his debut in a 3-1 win over their bitter rivals Liverpool FC to make the perfect start to his Manchester United career under Van Gaal.
Martial netted 19 goals in all competitions in his debut season at Manchester United but Mourinho’s appointment has seen Martial’s progress stunted at Old Trafford.
The French forward has been linked with a potential move to Tottenham in recent months, with Mauricio Pochettino a big admirer of the former Lyon striker.
Sky Sports News reporter Bridge believes Mourinho would be reluctant to sanction the sale of Martial to Tottenham considering their title potential.
“Tottenham like Martial a lot,” Bridge told the Transfer Talk podcast.
“Mourinho would prefer Martial to leave the Premier League if he were to leave.”
Manchester United finished in second place in the Premier League table last season to secure a spot in the Champions League.
The Red Devils have signed Shakhtar Donetsk midfielder Fred and FC Porto defender Diogo Dalot in the summer transfer window.
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