The Manchester Evening News says Martial is moving freely and without a brace on his injured knee, as the United forward targets a return from injury.
Martial was spotted out in the Manchester district of Hale with his wife Melanie, on Wednesday. The Frenchman was asked how his knee was recovering and replied that he was feeling good.
And he could yet play a part again this season for United, despite manager Ole Gunnar Solskjaer previously suggesting the 25-year-old's season was over. Martial picked up the injury during the international break at the start of this month, playing for France against Kazakhstan.
Martial has scored just seven goals in all competitions this season, four of them in the Premier League.