Besiktas president Fikret Orman has travelled to London to hold talks with Premier League clubs over current and future partnership deals.
The Black Eagles boss has made no secret of his desire to sign the out-of-favour striker.
“Benteke is a great player but he has a very high market valuation,” Orman was quoted as saying by Turkish-football.
Benteke’s agent Eris Kismet told Turkish-Football that the Black Eagles offered Benteke a personal deal worth £3.91 million and that his client would be keen on the move.
Besiktas could however, face competition from Crystal Palace who want Benteke on a permanent deal.
According to ESPN, the Reds have turned down Palace’s second bid for Benteke. The Eagles tabled a £23 million offer last week as Liverpool are determined to recoup the £32 million they signed him for from Aston Villa.
Benteke’s agent Erecently did recently tell 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.
Besiktas are in need of a replacement for Mario Gomez who revealed he will not be returning to the club this summer following the end of his loan deal from Fiorentina.
Gomez joined Besiktas as an out of form striker – much like Benteke – and left the top goal scorer in the league earning himself a return to the Germany national side where he scored twice at Euro 2016.
The experienced forward also played a key role in Besiktas winning the league title last season.