The Brazilian left-back has denied the Turkish club have made an offer for him but admitted he would consider what is best for his family if a proposal was forthcoming
The left-back denied any Turkish side had made an offer for his services despite speculation linking him with a return to the side he left in 2011 for the Emirates Stadium.
Santos has featured in only two Premier League games so far this season and has appeared only 17 times in total in the top flight for Arsenal since he arrived at the club.
"I would like to state clearly that I have a lot of respect for Fenerbahce, and I love Istanbul…but for now I am a Gunner," Santos said on his official Twitter page.
The strong early-season form of Kieran Gibbs has led to doubts over the Brazil international's long-term prospects in north London and he admitted he would consider what is best for his family if the chance to make a move did arise.
He added: "For now, I have not received an offer from a Turkish team. However, if I receive an offer one day, thinking what is best for my family, I will make a decision."