The Red Devils have been linked with a host of the Bavarians’ star names in recent months, with Arjen Robben, Toni Kroos and Thomas Muller having all had their names aligned with moves to Old Trafford.
Now Schweinsteiger is the latest player on LVG’s hit-list, with a £32m offer being mooted.
The Dutchman is said to have handed United a lengthy list of transfer targets to work on while he coaches Holland through the World Cup, with the German international near the very top.
The 29-year-old is widely seen as one of Bayern’s key men, and has been credited with playing a massive role for the club during their recent rise to prominence after being converted to a central midfield role from his original wing berth.
Van Gaal sees Schweinsteiger as the ideal man to overhaul his engine room, and the sort of player that was missing from the club last season as they slipped from Premier League champions to a side that will not be competing in European football of any kind during 2014/15.