The 32-year-old has a two-and-a-half-year contract on the table to move to the Turkish giants.
Galatasaray have until February 9 to close the deal, with the transfer window open in Turkey for eight days beyond the close of the Premier League's.
Cedric is ready to leave north London, having made just two senior appearances under Mikel Arteta this season. He has five months left on his current £70,000-a-week contract.
A move to Galatasaray would see Cedric link up with his former Gunners team-mate Lucas Torreira in a squad which also includes Chelsea loanee Hakim Ziyech, Tottenham loanee Tanguay Ndombele and former Crystal Palace star Wilfried Zaha.
Dries Mertens, Davinson Sanchez and Mauro Icardi also play for the Istanbul club.
Galatasaray are second in the Turkish Super Lig despite failing to win just four matches this season as they battle rivals Fenerbahce for the title.
Besiktas, who are led by former Portugal manager Fernando Santos, have also previously expressed an interest.
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