The 23-year-old is likely to miss most of the season after suffering anterior cruciate ligament damage in August while on international duty with Uruguay.
Despite a long road back to full fitness, Coates has been encouraged by his ongoing rehabilitation.
"I'm making progress slowly but surely," he told the club's official website. "It's an injury that takes a long time this one, and you have to work hard on a day-to-day basis to recover, but fortunately that's what I'm doing and so I hope to come back fit and well just as soon as I can.
"It's been going very well. It's a long recovery process for this injury and I think it's more about how you are psychologically in your head and trying to keep positive in order to be able to get back to full fitness as quickly as possible."
Liverpool continue their Premier League campaign on Sunday when they make the trip to Hull City.