The Turkish daily paper states that the Black Eagles have turned their attention towards Marseille goalkeeper Steve Mandanda as Ospina is reluctant to leave Arsenal.
Beşiktaş president Fikret Orman had confirmed interest in the Arsenal goalkeeper but Torunoğulları revealed that the north London based club have ruled out a move.
Torunoğulları said: “David Ospina is Arsenal’s second choice keeper and they are not letting him go in January there is no chance of this.”
Ospina fell down the pecking order at Arsenal following the signing of Petr Cech but he was expected to get some playing time after Wojciech Szczęsny was loaned out to Roma.
Arsenal take on Manchester City next Monday in a critical league encounter which could see the Gunners go top.
Beşiktaş are currently first in the Turkish Super League and managed by former Turkish national team head coach Şenol Güneş.