The Bavarians have been impressed with the Belgian defender during their Champions League matches against Arsenal and they are keen to lure him to Alianz Arena.
That is unlikely to be a difficult task given that Arsenal boss Arsene Wenger is looking to cash in on his captain in the summer transfer window.
Vermaelen has a contract until June 2015 at the Emirates, but it is believed he can be signed at a cut-price deal at the end of the season.
Meanwhile, the Bavarians are also looking at Shakhtar Donetsk defender Yaroslav Rakitskiy, who is also a left-footed defender.
Bayern officials are hoping to shake up their defensive options and they are interested in signing a player who can play at both centre-back and left-back.
Oddly enough, Thomas Vermaelen appears to be the more realistic target of the two and there is every chance the Bavarians will step up their interest in the Belgium international.