The Brazilian midfielder joined Atletico Madrid on a six-month deal back in January and has played a part in their march to the top of La Liga and the Champions League final.
It is not yet clear if he will remain at the Vicente Calderon, but Besiktas are keen to add him to their ranks.
Sources in Turkey claim they are willing to offer the 29-year-old a salary worth ?3.3m a season, but their interest also hinges upon whether they qualify for next season's Champions League.
Besiktas are currently one point adrift of a Champions League qualifying spot with two games of the domestic season remaining.
Southampton monitored his form earlier this season ahead of a possible free transfer move in the summer.
It is not yet clear if he will remain at the Vicente Calderon, but Besiktas are keen to add him to their ranks.
Sources in Turkey claim they are willing to offer the 29-year-old a salary worth ?3.3m a season, but their interest also hinges upon whether they qualify for next season's Champions League.
Besiktas are currently one point adrift of a Champions League qualifying spot with two games of the domestic season remaining.
Southampton monitored his form earlier this season ahead of a possible free transfer move in the summer.