However, Santos has revealed that manager Arsene Wenger was keen for him to stay and with that in mind, he believes that there is a chance that he will return to the Emirates Stadium.
"The idea is to go there, play well and be able to come back strong. Do I have a future at the club? For sure. This is a loan deal and after this season we will see where everything stands," he told the London Evening Standard.
"I always wanted to stay here until the end of my contract. This is a club where I feel comfortable and honoured to play. However, when the club acquired another left-back it was clear to me that I will not play. I need to play, get my confidence back and Gremio is a good platform for this.
"I talked [with Wenger] and we decided together this would be a good chance for me to get on top of my game. He gave me a hug and told me Arsenal would always welcome me back with open arms. He did [want me to stay] but he wanted to see me happy and if I am not performing all the time, then I am not happy."
Santos joined the Gunners in August 2011 from Fenerbahce.