Muller’s Bayern team-mate Toni Kroos and Borussia Dortmund pair Mats Hummels and Marco Reus have all been linked with Van Gaal, who will be confirmed as David Moyes’ successor next week.
But informed sources in Germany have revealed that Muller is the name at the top of Val Gaal’s wanted list and that he is the one manager the Germany striker would leave his home club for.
Muller is unhappy with his role on the fringes of Bayern’s starting line-up under Pep Guardiola and has become increasingly frustrated at being left on the bench for key games, such as the Bundesliga showdown with their main rivals Dortmund and Champions’ League tie against United.
Bavarian-born, he saw himself spending his entire career at the Allianz Arena but has been forced to contemplate the unthinkable of seeking a fresh start. According to sources close to him, Van Gaal’s imminent appointment as United boss has turned his sights towards Old Trafford.
While there have been widespread reports of some players being at odds with the Holland coach, due to his confrontational style, Muller readily concedes he owes his standing as one of Germany’s foremost forwards to the 62-year old.
As manager of Bayern, Van Gaal promoted Muller from the junior ranks and helped establish him as one of the Bundesliga’s most accomplished finishers.
Van Gaal has not forgotten how he responded to being given his opportunity and has been alerted to the stand-off that has developed between him and Guardiola.
Though United are not exactly short of strikers, with Robin Van Persie, Wayne Rooney, Danny Welbeck and Javier Hernandez all vying for places, Van Gaal is renowned for being single-minded about the players he wants and will not hesitate to move for Muller.
Persuading Bayern to do business may be a different matter. Under contract until 2017, Muller is hugely popular with team-mates and supporters, who see him as the face of the club due to his Bavarian roots and the way he graduated through the youth ranks.
But that won’t stop Van Gaal dipping into his massive transfer budget and trying to lure him to Old Trafford to form a new-look strike partnership alongside Van Persie.
Should he succeed, it would leave a further question mark against the future of Rooney, who would be left hoping Van Gaal might consider using him just behind the main strikers.