Martial came off the bench to score the decisive goal in Man United’s 2-1 victory over LASK in the Europa League Round of 16 second leg on Thursday.
He’s enjoying the highest-scoring season of his career with a tally of 23 goals in 46 appearances in all competitions.
The Frenchman is set to lead the line when United face Danish outfit FC Copenhagen in Lisbon on Monday and Solskjaer believes his physical improvement has made a telling impact.
“He’s in the gym a lot and he’s working on his fitness and strength. The fitness staff have done a fantastic job with him,” Solskjaer said.
Solskjaer added: “He’s physically at the best level in his career and I’m just looking forward to seeing him prove it even more because there is more to come from Anthony.”
The Europa League is their last chance at winning silverware this season, after finishing 3rd in the Premier League and the semi-finals in both the League Cup and FA Cup.
Man United have not gone three successive seasons without silverware since the 1988/89 campaign.
Martial has been crucial to helping guide United into the quarter-final with four goals in five games.
He’s also forged a strong relationship with fellow attackers Marcus Rashford and Mason Greenwood – with the trio scoring a combined total of 62 goals in all competitions.
Despite scoring 66 goals in 38 Premier League games, Solskjaer is reportedly set to strengthen their attacking line with the signing of Jadon Sancho.
The 20-year-old registered 20 goals and 20 assists in 32 appearances across all competitions last term.