Arsenal have offered Besiktas one of three players, David Ospina, Shkodran Mustafi or Danny Welbeck in addition to a lump sum for Besiktas defender Domagoj Vida according to the Aksam newspaper.
Per the source, Besiktas have snubbed the proposal and would only consider Ospina from the three players.
The Colombian keeper has been targeted by Besiktas as a replacement for Fabri who joined Fulham on a £5.3m move last month.
Black Eagles head coach Senol Gunes is fond of Welbeck but feels he has enough depth upfront.
The first round of talks between Besiktas and Arsenal ended with the Super Lig outfit offering a counterproposal demanding a £17.8m fee for the Croatia international defender.
The report claims that a Besiktas source informed them that Vida has a 50 percent chance of wearing an Arsenal shirt next season.
Vida returned to the Besiktas training grounds yesterday after enjoying an extended break following the World Cup.
The 29-year-old played an important role in Croatia reaching the final, scoring against Russia in the quarter-finals and providing an assist against eventual champions France.
Besiktas have given the green light to sell Vida despite only signing the defender in January, on a free transfer from Dynamo Kiev.
The defender does have another four-years remaining on his contract but Besiktas are aware his value has increased on the back of his World Cup display and are keen on cashing in.