The Sun reported yesterday that Besiktas set to offer Liverpool £12m for Simon Mignolet.
Per the source, Jurgen Klopp is prepared to let Mignolet leave for the right price following the transfer of Alisson.
The Belgium international meanwhile is aware of his situation that he has dropped down the pecking order, becoming third-choice keeper.
Liverpool will reportedly clear talks for Besiktas to hold talks with Mignolet later this week.
Sources close to Besiktas have informed Turkish-Football that while it is true the club have Mignolet on their shortlist as potential replacements for Fabri, who joined Fulham on a £5.3m move yesterday, the club will not offer £12m.
The Black Eagles hope to offer Mignolet a way out in the form of a loan move, potentially with a buyout clause option included in the deal.
The club would not be prepared to pay anything over £6million if they were to push for a permanent move.
The keeper has another three-years remaining on his contract but the Reds are keen on selling players this season to recoup some of the £170m invested in transfers this window.
Besiktas have already raised £12.45m from transfers this summer, a figure that could be set to triple should they sell Domagoj Vida for their asking price.
The Istanbul based side have money to invest this summer but their priority is to sign a high profile forward.
Besiktas do not view signing a new keeper as urgent as the need for a new forward.