The report claims that the Lions are targeting Ospina as a potential replacement for Fernando Muslera should he leave at the end of the season.
Ospina was closely linked with a move to Turkey at the start of the season and in January after Besiktas expressed an interest in the Colombian international.
The Black Eagles signed Boyko instead after Arsenal refused to sell their number 2 goalkeeper.
The Gunners may however, be prepared to part ways with Ospina over the summer as Arsene Wenger plans his overhaul of the squad.
Galatasaray will be without European football next season due to their UEFA ban for breaching financial fair play regulations.
Last seasons champions are having a nightmare season and will finish outside the top four but could still win the Turkish Cup as they have booked a place in the final.