The Belgium international striker is set for a summer exit after falling out of favour with Reds head coach Jurgen Klopp.
The Liverpool manager dropped Benteke from the squad going into the 4-3 win over Arsenal at the Emirates on Sunday.
Besiktas vice-president Ahmet Nur Cebi has already confirmed that the Black Eagles want Benteke on loan.
“Benteke is a player we are interested, we are pushing for him and would want him to be transferred to the club.” Cebi revealed to Turkish-Football.
Black Eagles president Fikret Orman also confirmed that he wants Benteke at the club but revealed that the transfer will not be easy to pull off.
“Benteke is a great player but he has a very high market valuation,” Orman was quoted as saying by Turkish-football.
“I want Benteke but Liverpool want a lot for him, it won’t be an easy transfer but we will see.”
Liverpool do however, want to sell Benteke on a permanent deal but have not had their asking price matched.
Crystal Palace have been in talks with Liverpool over Benteke but the Reds want £32 million for the Belgium international according to the Mirror.
Benteke’s agent Eris Kismet recently told Turkish-football.com, that the Reds asking price was putting clubs off.
“Liverpool want to sell Benteke but clubs that are interested as unable to match his valuation,” Kismet said.
Liverpool may consider a loan offer from Besiktas if their asking price is not met going into the last week of August.
Benteke does not feature in Klopp’s plans this season and if the Reds fail to move him on he will prove to be an expensive reserve.
The powerful striker scored 10 goals in all competitions for the Reds last season and has another four-years left on his contract.