The young forward is making a name for himself while playing for Bayern's Under-16 side and caught the eye with two goals in a recent UEFA Youth League clash against Tottenham.
The 16-year-old is said to one of the hottest prospects in Germany and the Bavarians are trying their best to secure his future as the vultures start to hover.
Bayern snapped Gunther up from Augsburg in 2016 and he has gone from strength-to-strength, earning comparisons to Bayern legend Arjen Robben, who has just left the club.
That is due to the fact that he plays down the right while being left-footed.
Unlike Robben though, he is also over 6ft tall, which means there is the option to play Gunther as an out-and-out striker in the future, making him even more attractive.
Gunther has bagged four goals in nine appearances so far this season and reports are claiming that Milan will do their best to try and lure him away.
Milan are having to work under tight financial constraints and believe Gunther is definitely worth a punt as he could be picked up relatively cheaply and could be a star of the future.
Bayern are well aware of that and could look to get him tied down to his first professional contract at the first opportunity.