With Radamel Falcao widely tipped to leave Atletico during the summer, reports have linked the Spanish outfit with a host of replacements.
However, according to agent Ali Egesel, Atletico have identified 27-year-old Yilmaz as the ideal candidate.
"We know that Atletico are interested. Burak knows that they are a big team," he told AS. "For him, La Liga is the best competition in the world and Atletico are in the top three."
Yilmaz joined Gala from Trabzonspor in July 2012.