The Brazilian left-back has made just 17 appearances since joining the Gunners form the Turkish giants last summer and has been linked with the possibility of heading back to Istanbul.
Santos denied that there had been an offer from a Turkish club for his services but did indicate that he would consider any proposal that came his way.
"I would like to state clearly that I have a lot of respect for Fenerbache, and I love Istanbul but for now I am a Gunner," Santos posted on Twitter.
"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."