The Lions will enter talks with Campbell over the winter transfer window over the possibility of a transfer to the reigning champions.
The Istanbul giants have been closely linked with the Costa Rica international in the past but Arsenal boss Arsene Wenger has moved out all previous offers for a permanent move and only allowed him to leave on loan.
Despite struggling to get any playing time this season Campbell’s patience was recently rewarded when Wenger decided to start him against Bayern Munich in the Champions League and on the weekend against Tottenham in the North London derby.
Campbell has just a year remaining on his contract meaning Galatasaray could enter direct talks with the 23-year-old should Arsenal decide not to extend his current deal.
Galatasaray are the reigning Turkish Super League champions and are currently competing in the Champions League group stages which would mean Campbell would be cup tied should the Lions progress to the next round.