Italian outlet Tuttosport, as quoted by Metro, is reporting that the 22-year-old French striker has been consulting with his compatriot about the possibility of joining Juve this summer.
Martial will have one year left on his contract at Manchester United at the end of the season, although the Red Devils are thought to have the option to extend his current deal by a further 12 months.
According to the same story, the appeal of joining Juventus has increased for Martial in recent weeks after speaking with his French team-mate Matuidi about the Italian club during the international break.
Martial has been in and out of the Manchester United team under Jose Mourinho this season.
The striker has scored nine goals and made five assists in 26 Premier League games so far this term but he has only started 16 of those matches.
The attacker will be hoping to start for Manchester United when the Red Devils host Swansea City at Old Trafford in the Premier League on Saturday.
The Red Devils are currently in second place in the Premier League table.
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