The Frenchman is set to hold talks with Manchester United over a new long-term deal, according to The Sun.
Anthony Martial barely played for the Red Devils during the first half of last season, and he was loaned out to Sevilla at the turn of the year.
After an unsuccessful spell in La Liga, there were suggestions that he could be offloaded by United, but things have turned out differently.
The 26-year-old was in fine form under new manager Erik ten Hag during pre-season, registering three goals from just five appearances.
He has been largely injured since the new campaign, but registered a match-winning assist off the bench in the recent 2-1 victory over Liverpool.
It is now reported that the club are planning to hold talks over a new deal with Martial, who has less than two years left on his current contract.
The Red Devils have the option for another 12 months, but the hierarchy want to protect their investment by commitment him to a fresh extension.
Ten Hag also views the £36 million signing as a key part of his plans at the club.
Anthony Martial has a big future ahead under Erik ten Hag
When Ten Hag was appointed as United’s manager, there were doubts whether Martial would fit into his plans after an unsuccessful loan stint.
Martial was the subject of criticism from some fans for his languid playing style, but he has made tremendous improvement under Ten Hag.
There has been a definite increase in his work rate and high pressing. His ability to provide key passes makes him a perfect fit for the head coach.
At 26, Martial is currently in the prime of his career, and has the opportunity to lead the attack regularly if he can get over his recent injury record.
It does not appear much of a concern with minor setbacks, but he needs to stay unscathed over long periods to establish himself as a starter.
Martial is presently on a weekly package of £250,000, and a new contract could potentially see him enter the £300,000-a-week bracket for United.