Martial has been out of action since picking up a knee injury while on international duty with France in March.
It meant that the centre-forward missed the final months of the club season and the chance to represent his country during Euro 2020.
Solskjaer has revealed that the Frenchman is building up his fitness at Carrington and is now close to a return to full training.
Meanwhile, the Norwegian has revealed that a few other players appear close to returning ahead of the club’s final two pre-season friendlies.
“Dean (Henderson) is back in training, “he said, “Diogo (Dalot) and Donny (van de Beek) have trained and they’re ready to play a part…I would think they’ll be subs.”
Reds’ talisman Bruno Fernandes is also said to be back in training, although tonight’s game against newly promoted Brentford will come too soon for him to feature.
Solskjaer said, “Bruno is back in training. He’s not ready to join the Brentford game…but he’s not too far.”
Midfielder Scott McTominay is also said to be close to a return following his Euros exploits with Scotland.
However, there were some clouds to blot the otherwise sunny outlook, with Alex Telles out for a few weeks with an ankle problem.
The injury puts extra pressure on the fitness of Luke Shaw, who is himself recovering from broken ribs sustained while on international duty with England.