The Brazil international spent the second half of last season on loan at Gremio and his chances at the Emirates Stadium look bleak with both Nacho Monreal and Kieran Gibbs ahead of him in the fight for the left-back spot.
Santos only made 12 appearances under Arsene Wenger last season and was sent out on loan in January. He impressed with Gremio but Flamengo have now emerged as favourites to sign the 30-year-old.
Flamengo coach Mano Menezes worked with the full back during his brief spell at Corinthians and the club's director of football Paulo Pelaipe is hoping to have the deal agreed before the Brazilian transfer window closes on July 20.
"The negotiation is well under way, but we have the transfer window problem as it's about to close," he told UOL. "We are waiting for a signal from Arsenal.
"I don't want to talk about optimism or pessimism, as I don't want to make the fans create expectations.
"But if Arsenal accepted to talk with us and listen to offers, I think we won't have problems, let's wait."