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The 31-year-old, who has previously represented Napoli and Atletico Madrid, played 31 times in the Super Lig as Besiktas were crowned champions last season, scoring seven goals.
Sosa is eager to move on with Milan in negotiations to sign him ahead of the 2016-17 season.
However, reports suggest the two teams are some distance apart over a potential transfer fee even though personal terms with the player are settled.
"It is a proposal that comes from a great team," Sosa said to Fanatik.
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"Such opportunities do not always come and I do not want to miss the chance to play for Milan."
Milan only have two new arrivals so far ahead of the new Serie A campaign – striker Gianluca Lapadula and defender Leonel Vangioni.