The Germany international has recently emerged as a top target for the reigning Premier League champions, with incoming manager Louis van Gaal having been linked with a £25m raid for the attacker.
But now Liverpool and Arsenal are in the fight amid speculation that Muller has grown disillusioned with life at the Allianz Arena.
Despite being a fans’ favourite and an academy graduate, the 24-year-old has featured infrequently under Pep Guardiola this term, with a large chunk of his outings having come from the bench.
With his peak years just coming onto the horizon, the versatile ace is rumoured to be targeting regular action, and could well leave in order to find it.
Liverpool and Arsenal are believed to be watching closely, and have even asked to be kept informed of the situation ahead of a possible three-way bidding war for the player.
The Gunners are known to be looking for a guaranteed source of goals, while Brendan Rodgers needs to add quality to his squad after booking a spot in the Champions League for next season.
United may well hold a trump card in van Gaal’s relationship with the player, but a lack of top level European football could be a factor that works against them.