United face Villarreal in the Europa League final on May 26 and Solskjaer is hopeful of having his captain available.
"He's making progress but we've consciously taken the route of not testing him out too early, too quickly, because we don't want to aggravate something," Solskjaer told a news conference on Sunday.
"He wants this so much, so he doesn't want to take any risks either. When I spoke to him this morning, he was quite positive. But, naturally, the day after it happened we were all down.
"But we saw early on or decided we have to focus, have to be positive and think that you're going to make it until you have to say 'no.' I've always been an optimist, so we're positive."
Maguire will almost certainly start in Gdansk if he is passed fit but Solskjaer has a number of tough choices to make before deciding on his starting XI for United's first final since 2018.
"It is always difficult," Solskjaer added, who was left out of Sir Alex Ferguson's starting lineup for the 1999 Champions League final before coming off the bench to score the winner.
"The human side of you, you want everyone to get the experience but then you have to pick 11. That's just the perks or nature of this job that you have to make some tough decisions and you have to stand by them and we've still got a couple of games left in the league to finalise what the 11 in the final will be.
"You'll have to sit down, of course, individually, and I remember Sir Alex sat me down, he came to my hotel room to explain why I didn't play the semifinal against Bayer Leverkusen and we sat there for 45 minutes, we had a good conversation and I still felt I had a contribution to make and that I was important in his team.
"All my players, they know that they have been important for us this season, we couldn't get to a final, second place in the league, without everyone's contribution every day because that's the culture we are in. They've been competitive but they've been very supportive as well."