Besiktas have been linked with the former Chelsea and Real Madrid midfielder Lassana Diarra.
The Black Eagles have already signed a Milosevic from AIK Stockholm this month and are looking to add a right back and defensive midfielder to their squad.
Slaven Bilic has recommended the French international who is currently a free agent to the club.
Inter and Celtic have also expressed an interest in the 29-year-old.
Besiktas have also been linked with Tolgay Arslan and Gokhan Inler in recent weeks.
Diarra has previously played for Arsenal, Chelsea, Real Madrid, Anzhi and Lokomotiv Moscow.
The French international made 21 appearances for Lokomotiv Moscow last season.