Martial scored his 23rd goal for United in all competitions this season against LASK Linz in Wednesday's Europa League last-16 victory.
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"Anthony has made huge strides this season in many aspects of his game," Solskjaer told an eve-of-match news conference ahead of Monday's Europa League quarter-final clash with Copenhagen in Cologne.
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"Physically, he is at the best level of his career. We know he can do worldies but I like him scoring the simple goals, when he is in between the posts. He's done that a few times.
"He's in the gym a lot working on his fitness and strength. I'm just looking forward to seeing him improve. There's more to come from him."
Solskjaer added the he was delighted with Pogba's return to form after persistent injury problems plagued his 2019-20 campaign.
"We're delighted that he, he's back playing, he's fit, he's enjoying his football," Solskjaer said. "Of course, he's... got to make up for lost time and he's trying to do that. He's training extra.
He's always a great personality in and around the place and hopefully we can see him, lift this trophy that he's done before. He is professional, he's a fantastic boy and I'm delighted that we've got him in the team.
United arrived earlier on Sunday for the remainder of the Europa League tournament, which will feature one-match knockout ties at different German venues, culminating in the final, also in Cologne, on August 21.
Jesse Lingard of Manchester United celebrates scoring their first goal during the UEFA Europa League round of 16 second leg match between Manchester United and LASK at Old Trafford on August 05, 2020 in Manchester, England.
Image credit: Getty Images
Solskjaer, who has already guided United to Champions League qualification with a third-placed finish in the Premier League, said the end-of-season event will aid his side's development.
"We went into this season knowing that Europa League is a great chance for us to get a trophy, to get far in a tournament," he added.
"But also to groom a few of the youngsters and it was perfect for us.
"I think if we'd been in the Champions League, I maybe wouldn't have had the chance to play the likes of Brandon (Williams), Mason (Greenwood), so many of the young kids who have now started what's going to be fantastic careers."