Schweinsteiger missed the 3-1 win against Barcelona due to injury but will be keen to play against PSG to build up match fitness ahead of the new campaign.
Man United fans will also want to see the German as he has become an instant favourite at Old Trafford since he completed his move from Bayern Munich earlier this month.
Van Gaal indicated he is hopeful Schweinsteiger will be fit but offered no guarantees.
Asides from LVG press conference. Thinks Schweinsteiger will be fit for PSG on Wednesday and still 'hopes' De Gea will stay.
— Rob Dawson (@RobDawsonESPN) July 25, 2015
Schweinsteiger suffered a few injuries at Bayern last season and the hope is that his current knock isn’t too serious.
Regardless, United finally have some options in midfield so it will be easy to rotate again should the 30-year-old miss out. Morgan Schneiderlin, Michael Carrick, Ander Herrera and Daley Blind are all more than capable of filling in for him.