Besiktas manager Senol Gunes has given the board the green light to push ahead with efforts to sign a new goalkeeper a source close to the club revealed to Turkish-Football.
Liverpool keeper duo Simon Mignolet and Loris Karius are the two shot-stoppers being targeted.
Gunes had initially hinted he would be prepared to keep Tolga Zengin on as his first choice shot-stopper.
The board also recently gave Zengin their backing in preparation for the possibility of not finding a replacement for Fabri who parted ways to join Fulham last month on a £5.3m move.
Zengin has however, had a disappointing start to the season and signing a new keeper has been made a top transfer priority.
Besiktas initially had a four-man keeper shortlist including David Ospina, Harun Tekin and Liverpool duo Simon Mignolet as well as Loris Karius.
Ospina has since joined Napoli on loan, meanwhile, the Black Eagles have abandoned plans to sign Tekin after failing to agree a transfer fee.
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The Black Eagles feel their bargaining position has strengthened since Napoli signed Ospina.
Additionally, the Serie A transfer window shuts tonight while Super Lig sides have until 1 September to complete their moves.
Mignolet and Karius are being targeted by Besiktas on loan moves.
The Belgium international has dropped into third place in the pecking order behind Alisson Becker and Loris Karius.
The Reds are keen on selling Mignolet but Besiktas are only interested in a loan move.
The Black Eagles are of the view that they currently have a higher chance of signing Karius on a loan move.
Liverpool have long-term plans for the keeper but feel he could do with playing first-team football this season and regaining his confidence.
Besiktas would be keen on either keeper as long as the Reds were to accept a loan move.
As things stand, intermediaries have been leading talks but the Black Eagles have yet to make a formal offer for either keeper.
