The Black Eagles have made an enquiry regarding the availability of the Ghanian international on a one-year loan.
Rahman could end up joining fellow Chelsea defender Kenneth Omeruo if he does end up making the move.
Omeruo is expected to join the Black Eagles on a one-year loan with a future buyout option.
Besiktas could however, face competition from Lazio for Rahman. The Serie A outfit are reported to be bidding £13 million for the 22-year-old according to the Daily Star.
Per the source, Rahman’s future at the club looks bleak and Chelsea are expected to give him the green light to leave.
The Blues may however, not want to sell Rahman on a permanent deal considering he joined on a £17 million move from Augsburg in 2015.
The young full-back used sparingly last season making just 23 appearances for Chelsea in all competitions last season.
Rahman does have another four-years remaining on his Chelsea contract but his future at the club under the stewardship of Antonio Conte remains in doubt.