Maguire was pictured on Thursday without crutches or a protective boot after damaging ankle ligaments in the 3-1 win over Aston Villa on May 9, raising hopes he might be available to face Villarreal in Gdansk on Wednesday but Solskjaer said it is unlikely.
"He's walking but it's a long way from walking to running," Solskjaer told a news conference of Maguire on Friday. "To be honest, I don't think we'll see him in Gdansk but I'm going to give him until Tuesday night and the last training session to be out there.
"He's improving but ligaments take time to heal. Anthony is not going be available; Scott and Fred should be OK."
United have two games left this season, starting with the trip to Wolverhampton Wanderers on Sunday followed by the first final of Solskjaer's reign. The Norwegian has overseen steady improvement at Old Trafford and despite a second place finish in the Premier League, he said the squad is still short of "two or three players" if they want to bridge the gap to champions Manchester City next season.
"I hope we're going to strengthen with two or three players," he said. "We definitely need to challenge higher up in the table, we're still too far behind to be honest.
"We've had a few players on loan that might come back in, there is interest in a few others going out but you want to come out of the transfer window strengthened and it might be we allow some players to go out and come back stronger from it. It's difficult to say, I can't see too many outgoings."
One player who could leave is Juan Mata, who is out of contract in the summer. Solskjaer has held talks with the Spaniard but says a decision will not be made until after the Europa League final.
"We're talking to Juan, we've had good dialogue, good discussions and that dialogue will continue, let's see what he wants to do at the end of the season," Solskjaer said.
"He's such a top professional, a very good player, it's hard for me not to play him more than I have done, there have been circumstances this season, personal issues that made him less available but still he is a top player. That decision will be made after the season is finished."