The German has not played a single minute for the Red Devils this season after being told by boss Jose Mourinho he did not feature in his plans on his arrival at Old Trafford.
However, the 2014 World Cup winner has impressed with his attitude in training in recent weeks and was on the bench for Sunday's 1-1 draw with the Hammers in the Premier League.
Mourinho is now considering whether to hand Schweinsteiger a start, as Paul Pogba and Marouane Fellaini are suspended for the quarter-final tie while Michael Carrick is an injury doubt.
The United boss is likely to make alterations from Sunday's side, with Luke Shaw and Anthony Martial hoping to earn recalls after being left out of the squad at the weekend.
Wayne Rooney and Henrikh Mkhitaryan could also come into the starting XI, having been on the bench, but Chris Smalling and Eric Bailly are still unavailable due to injury.