Brazilian outfit's executive director Rui Costa revealed on Saturday that the 29-year-old was traveling to Porto Alegre to finalise the terms on the year-long move back to his homeland.
Arsenal are yet to comment on the move but the full-back himself indicated a switch was close, with the Premier League outfit able to cut the deal short after six months if they wish.
"I have the best expectations," Santos told Lancenet. "[Gremio] are one of the biggest clubs in the country.
"I've come to Gremio to be a champion. I am very excited about this project. I have dreamed of working with Vanderlei Luxemburgo. He is a top manager in our football."
Santos admitted, though, that he would need time before reaching match fitness after a stop-start season at Arsenal.
"If there was a game today, I would like to play," he added.
"But I need to be match fit as I played a game one day, then not the next one. I'll need five or six games to be fitter. I'm anxious to know the squad."