The Holland coach is likely to be confirmed as David Moyes’ successor in the coming days, with rumours suggesting a deal between the club and the 62-year-old has been all but finalised.
After a below par campaign at Old Trafford United are set to undergo a massive summer of transfer business, with van Gaal due to be handed upwards of £150m to restructure the first-team squad.
He is already thought to have handed the club a set of targets, with Muller near the very top the list.
The skilful and versatile attacker has featured infrequently under Pep Guardiola this term, with the likes of Franck Ribery, Arjen Robben and Mario Mandzukic having kept him out of his star-studded starting XI.
The 24-year-old has spent his entire career with the Bavarian giants, yet he is thought to now be considering his options as he targets guaranteed action for the peak years of his career.
Having worked with van Gaal at Bayern a link-up could be appealing to the German, who knows that his chances of playing time will be massively increased at the Theatre of Dreams.