The midfielder has reportedly been recuperating in Dubai and is not expected to fly to Germany on Tuesday with the squad.
If the 21-year-old does not make the flight to Bavaria, with the Gunners trailing 3-1 from the last-16's first leg, he is also likely to miss the Premier League trip to Swansea on Saturday.
Wilshere is also in danger of being ruled out of England's World Cup qualifying double-header in San Marino and Montenegro, which starts a week on Friday.
Roy Hodgson will select his England squad on Thursday but may face a wrangle with Wilshere's club boss Arsene Wenger if he picks the injured playmaker.
Wenger was angry after Wilshere played the whole 90 minutes in last month's friendly victory over Brazil at Wembley.
The Frenchman felt he had an agreement with Hodgson that Wilshere would not play the full friendly against the South Americans.
Wenger also clashed with the national boss in November after Hodgson selected Wilshere in the squad to face Sweden in a friendly after he had recently returned to first team action following his serious ankle injury.
England U21 coach Stuart Pearce bowed to pressure from the Gunners and omitted Wilshere when he was in charge of Team GB at last summer's Olympics.