Ali Egesel has revealed that the Spanish club have already informed him of their keenness to land the 27-year-old, adding that "some Italian teams" are also monitoring the Turkey international.
"It is true that there is particular interest from Atletico," he told Tuttomercatoweb.com. "But there are other possibilities.
"There are also some Italian teams interested. Last season he nearly joined Lazio, but I do not want to name names.
"Burak is happy at Galatasaray, but if an offer came in then we are willing to listen."
Yilmaz has scored 18 goals for Galatasaray in the Turkish Super Lig and was an important player in his side's progress to the Champions League quarter-finals this season.