Lutfi Aribogan claims that the Gunners left-back is on the Turkish giants' list of potential recruits but they are yet to make contact with the Brazilian or his club.
The defender has failed to fully establish himself in the Premier League, and seen his appearances once again limited so far this season by injury and the good early form of Kieran Gibbs.
Santos has also lost his place in the Brazil set-up under Mano Menezes, not featuring since the Copa America in 2011, and could be in search of regular first-team action in anticipation of World Cup 2014, which will be held in his home country.
"Andre Santos is one of the names [we have] on our list,"
Aribogan told the Turkish sports newspaper Fanatik. Galatasaray are familiar with Santos from his stint with Super Lig rivals Fenerbahce, where he spent two seasons prior to signing for Arsenal, and it seems that a return to Turkey could perhaps be on the cards for the Brazilian.
However, Aribogan did admit that any possible transfer is, at the moment, a long way off, adding: "We currently have no contact with his club and the player himself."