Martial scored the equaliser as United earned a 1-1 draw at Club Brugge in the first leg of their Europa League last 32 tie on Thursday, upping his goals tally for the campaign to 14 in all competitions.
The 24-year-old is three shy of his best return from his debut campaign with United in 2015-16, when he became the most expensive teenager in world football after arriving from Monaco for an initial fee of £36 million ($46.5 million).
“I think Anthony can step up and get a few more and get to the 20 mark. Definitely,” said Solskjaer.
“He’s got quality of course, he’s a very good finisher. He takes his chances really well. There’s good technique in his finishing. He’s good receiving the ball at times and dropping off.
“He can play almost like a false nine as well. Sometimes I’d like him to be stronger physically.”
Martial has often struggled to cope with the lofty expectations at Old Trafford, but Solskjaer’s admission that Rashford could be sidelined until next season with a back injury leaves the Frenchman facing increased responsibility as United attempt to secure Champions League qualification.
“He’s confident in front of goal now,” Solskjaer said of Martial, who also scored a superb header in the 2-0 away defeat of Chelsea in the Premier League on Monday.
“That was a 1980s centre-forward goal. I’m encouraged by his attitude this season as well, wanting to do those things that are not natural for him. You’ve got to make him a number nine again after playing wide for so many years. Anthony and Marcus have played wide for a few years until the last 12 months really.”
Martial almost added a second before half-time in sodden conditions in Bruges with a curling 20-yard strike that Simon Mignolet tipped on to the post, but it wasn’t until the late introduction of January signing Bruno Fernandes that United really took control.
“He made a difference in the 10 or 15 minutes he played,” said Solskjaer.
“I didn’t really want to play him, but we had to settle down and create chances. We were close to winning and he’s done something for everyone, coming in.
“It’s important that we give him time to settle in, but we needed to get more on the ball and get more composed and hopefully get the goal. He created some chances and showed what he can do.”
United again have just two days to recover ahead of the visit of Watford on Sunday, but they could be boosted by the return of Scott McTominay, the Scottish midfielder out with a knee injury since late December.