The Old Lady want to take full advantage of in-form Martial's uncertain future at Manchester United by offering him a lucrative contract.
The Frenchman is refusing to put pen-to-paper on a new contract at Old Trafford with his current deal expiring next summer.
United do have a clause in his contract that gives them the option of triggering his stay for an extra year.
But it won't prevent the Italian champions from making their move, report TuttoSport.
They know that Martial remains unhappy at the Red Devils under boss Jose Mourinho despite his resurgence in form in recent weeks.
The 22-year-old, who was left out of the France World Cup winning squad, has scored five in his last five matches.
He will also have the chance to put in the perfect audition when the Red Devils meet Juventus in the Champions League tonight.
Juve are also plotting an ambitious move for Borussia Dortmund and England wonderkid Sancho.
Sancho, 18, only recently penned a new five-year contract extension and would only consider flogging him if they received an offer they couldn't refuse.
The report claims that Dortmund will hold out for £70million despite his young age.
His rise has been meteoric in the Bundesliga after ditching Manchester City in 2017.
Sancho has bagged four goals and six assists in four league starts and has already been linked with a move back to the Premier League.
Gareth Southgate rewarded his huge potential by awarding him his first England cap last month.
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