The German international has been linked with a move to Old Trafford as boss Louis Van Gaal looks to be reunited with the player he coached whilst in Germany.
And after Muller confirmed he is willing to listen to transfer offers, United have been quick to seize their chance to bring the Bundesliga star to the Premier League.
It is thought that the German champions do not want to sell their prize forward and have already rejected the bid, but United still remain hopeful they can do business.
Van Gaal is in the market looking for another forward after they saw their bid for Palermo forward Paulo Dybala dismissed.
By Phil Wellbrook