United captain Maguire limped off with ligament damage sustained in an awkward collision with Anwar El Ghazi during Sunday's 3-1 win at Aston Villa.
That raised fears England centre-back Maguire could miss United's European final against Villarreal in Gdansk later this month and the delayed Euro 2020, which starts in June. But, speaking ahead of United's Premier League clash with Leicester, Solskjaer offered hope that Maguire could return for the final.
"There's no fracture. There is ligament damage but hopefully we'll see him again this season and hopefully he will be ready for the final," Solskjaer told MUTV.
Maguire's absence from the match against his former club Leicester meant the centre-back was missing his first Premier League fixture since joining United in 2019.