The Brazilian full-back turned down the opportunity to return to Turkey - snubbing an offer from Turkish giants Galatasaray.
Santos has endured a terrible few months with the Gunners, and has proved to be a lightning rod for criticism of Arsene Wenger's side.
The 29-year-old has struggled to hold down a first-team place, and injury to Kieran Gibbs last month even prompted Wenger into the last-minute purchase of Spain fullback Nacho Monreal.
And it seems the Gunners boss was prepared to let Santos leave last month - with Galatasaray ready to bring him back to Turkish football.
The ex-Corinthians star spent two years with Fenerbahce between 2009 and 2011, and impressed enough to earn a £6m move to the Emirates Stadium.
But the Brazilian, who has 22 caps for his country, wants to stay and fight for his place at Arsenal after falling out-of-favour.
The report claims Galatasaray will renew their interest in Santos at the end of the season, and with new £8m man Monreal and England international Gibbs now in front of him at left-back, a move to the Turkish club could be on the cards again in the summer.
Monreal made his Arsenal debut against Stoke City on Saturday, and looked composed against a physical side as the Gunners ran out 1-0 winners thanks to a late Lukas Podolski free-kick.
The former-Malaga man has a handful of Spain caps, and the 26-year-old has all the makings of a solid player for his new club.