The Brazilian full-back returned to his homeland in January after struggling to settle in England.
An early-season loss of form convinced Arsene Wenger to let him head out on loan, with Nacho Monreal drafted in as cover during the winter transfer window.
Santos announced on his departure from the Emirates that he intended to return and prove himself to the Gunners faithful.
He has, however, relaxed that stance since returning to familiar surroundings.
The 30-year-old now says that he would welcome the opportunity to remain at Gremio past the end of the season.
Santos told Zero Hora: "I'll do my best to win titles. I have won titles at every club I have played for.
"The staff, board and the players have all made me feel very welcome. There is no doubt that I want to stay."