The Turkish Süper Lig broadcaster report that the Yellow Canaries have agreed terms with the Colombian international and all that remains is for the clubs to agree on a transfer fee.
The Czech Republic international looks certain to join the Gunners over the summer transfer window and will become the North London based clubs highest paid transfer according to the Metro.
Ospina joined Arsenal from Ligue 1 outfit Nice last season and kept 10 clean sheets in 23 appearances for the Gunners.
The Colombian international is currently on international duty with Colombia at the Copa America.
The Yellow Canaries have been targeting a new goalkeeper after recently appointed sporting director Giuliano Terraneo revealed Volkan Demirel would not keep his place as first-choice keeper next season.