Harry Maguire is facing a fitness race to make the Europa League final against Villarreal on May 26 after suffering ankle ligament damage.
The Manchester United captain was injured in a collision with Anwar El Ghazi in the second half of United's 3-1 win at Aston Villa on Sunday.
The centre-back was replaced by Eric Bailly, meaning he did not complete 90 minutes for the first time in the Premier League since joining United (72 games).
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Maguire was seen watching Tuesday night's Premier League game with Leicester from the directors' box at Old Trafford, wearing a protective boot and walking with crutches.
He is also likely to miss United's final matches of the league campaign against Liverpool, Fulham and Wolves.
"He's obviously had the scans and the good news is there is no fracture," Ole Solskjaer told MUTV ahead of the Leicester game.
"[There's] ligament damage but hopefully we will see him again this season. Hopefully, he'll be ready for the final."
England take on Austria on June 2 and play Romania four days later, with their European Championship campaign starting against Croatia at Wembley on June 13.
Sky Sports News expect England manager Gareth Southgate to name his squad for the Euros on May 25.