The 25-year-old has been ruled out since March with a knee injury, sustained whilst representing France during a World Cup qualifier against Kazakhstan.
Martial, who was ruled out of Euro 2020, has since been linked with a potential move away from Old Trafford this summer, following the arrival of Jadon Sancho from Borussia Dortmund.
Tottenham Hotspur are understood to be monitoring the forward, who United would be willing to sell for a fee in the region of £50m.
Solskjaer, however, has revealed that Martial is one of several first-team players who has returned to the club after a spell on holiday and the Norwegian is hopeful that the Frenchman can begin training soon.
"Anthony Martial has also joined us, but he's not joined the team training yet. He's recovering from the knee injury and that looks good. The rest of them will drop in after their well-earned holidays because some of them needed them and they deserved them," Solskjaer told Man United's official website.
Martial, who still has three years remaining on his current contract, has made 258 appearances for the Red Devils since joining the club from Monaco in 2015, scoring 78 goals and providing 50 assists. body check tags ::