Maguire sustained ankle ligament damage during United’s 3-1 win at Aston Villa on May 9, and has been sidelined since then.
“Of course [Maguire] wants to play,” Solskjaer said. “It’s going to be up to the doctor to say how he is, but I don’t expect him to be ready.
“It doesn’t look great, but ever the optimist, I’m still hopeful.”
Maguire’s likely absence means either Axel Tuanzebe or Eric Bailly will partner Victor Lindelof at centre-back, with Aaron Wan-Bissaka and Luke Shaw at full-back.
In goal, Dean Henderson has become the No1 goalkeeper meaning David De Gea has taken on cup duties, so that should see the Spaniard start in Poland have played in the semi-finals against AS Roma.
In midfield, Fred and Scott McTominay are slight doubts but should play holding roles.
Further ahead, three players – Bruno Fernandes, Edinson Cavani and Paul Pogba – are certain starters.
Pogba has edged ahead of Marcus Rashford as the favoured attacker on the left, while Mason Greenwood’s impressive form has seen him favoured on the right – and that could mean Rashford has to settle for a place on the bench.
Anthony Martial and Phil Jones remain sidelined by injury, while Dan Jones returned with an assist against Wolves.
Anthony Elanga scored his first senior United goal on his Premier League debut at Molineux. While the 19-year-old will not start, he could well come on if United need a goal.
Man Utd predicted lineup:(4-2-3-1) De Gea; Wan-Bissaka, Tuanzebe, Lindelof, Shaw; McTominay, Fred; Greenwood, Fernandes, Pogba; Cavani
Injury list: Jones, Martial
Doubts: Maguire, Fred, McTominay
Man Utd Europa League squad
Goalkeepers: David De Gea, Dean Henderson, Lee Grant, Nathan Bishop
Defenders: Eric Bailly, Victor Lindelof, Harry Maguire, Luke Shaw, Alex Telles, Axel Tuanzebe, Aaron Wan-Bissaka, Brandon Williams
Midfielders: Amad, Bruno Fernandes, Fred, Daniel James, Juan Mata, Nemanja Matic, Scott McTominay, Paul Pogba, Donny van de Beek
Forwards: Edinson Cavani, Anthony Elanga, Mason Greenwood, Marcus Rashford, Shola Shoretire