The 28-year-old was forced off with damage to ankle ligaments against Aston Villa on May 9, and he was seen in the stands on crutches during the visit of his former club Leicester City two days later.
Solskjaer was initially optimistic that Maguire would be back for the Europa League final against Villarreal, but the United boss has now offered a less-than-positive update on the centre-back's situation.
Speaking to reporters ahead of Man United's clash with Fulham on Tuesday, Solskjaer said: "It's still too early. We're not at the testing stage yet.
"We'll give him as much time as possible to recover. We're not going to see him back in the league so hopefully we can welcome him back for the final, but I'm not sure."
Maguire's fellow centre-back Phil Jones joins him in the treatment room, but Solskjaer is hopeful that attacking duo Anthony Martial and Daniel James will be able to play a part against Villarreal. body check tags ::