Talks with the France winger have been ongoing for more than a year but look to be nearing a conclusion, according to ESPN.
Old Trafford chiefs are confident Martial, who has been rejuvenated under interim chief Ole Gunnar Solskjaer despite a telling off for being late, will put pen to paper.
Especially after a "significant step" in talks over the last two weeks.
This a complete U-turn from the summer when club bosses feared he would seek a move away from Manchester.
That was why they triggered a one-year option to keep the 23-year-old where he is until 2020.
It is believed talks have taken so long to reach a resolution because of the arrival of Alexis Sanchez, which pushed Martial down the pecking order.
The Frenchman's form has been so good this season, however, that he has kept Sanchez and Romelu Lukaku out of the side.
De Gea, 28, regarded by many as the greatest keeper in the world, has a deal until 2020 and has reportedly been offered a new five-year deal to ward off Real Madrid once and for all.
The Spaniard is set to earn around £400,000 a week as part of the deal, which will make him the best paid goalkeeper in football.
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