The Bayern Munich star is part on a long-list of players Van Gaal wants to bring to Old Trafford.
But the German playmaker is likely to cost United around £50m and will only be tempted if they qualify for the Champions League this term.
Despite spending £150m last summer, Old Trafford bosses have handed Van Gaal a colossal war chest of £200m to spend next year with the hope that a return to the Champions League will enable them to sign some top-quality players.
Starsport today revealed how United bigwigs want to revolutionise the squad and bring in a fresh crop of world-class talent which would give them two quality players in each position.
United signed six players last summer and hope to pull of a similar trick before the start of the 2015/16 season.
Radamel Falcao, Angel di Maria, Daley Blind, Marcos Rojo, Luke Shaw and Ander Herrera all joined the Red Devils and Van Gaal wants a similar number next season.