Chelsea signed the 18-year-old midfielder from Santos in the winter transfer window after beating competition from several clubs in Europe.
Santos recently led the Brazil Under-20 side to the South American Championship but he is yet to make his debut for Chelsea.
He is yet to receive a work permit and Chelsea have been considering a contingency plan of loaning him out.
Several Brazilian clubs are interested in taking him back to his homeland, but according to Turkish outlet Fotomac, Besiktas are also in the race.
The Turkish giants have their eyes on the teenage midfielder with a view to potentially signing him.
Besiktas are claimed to be interested in getting their hands on him on a year-long loan deal.
It is unclear whether they are trying to sign Santos before the transfer window closes in Turkey in March or wait until the summer.
Chelsea have been confident of securing a work permit for Santos but loaning him out is an option they are prepared to consider.
