The 22-year-old tore a ligament while on international duty against Japan last week.
"He picked up a similar injury to what Martin Skrtel had last year so it's probably going to rule him out for most of the season, which is disappointing for me because he's never given me a minute's problem since he's been here," Rodgers said at a news conference.
"This was probably a year he needed to go out and play, so unfortunately this will put an end to that,"
Coates has made 12 league appearances since joining Liverpool from Nacional in 2011, scoring once.
According to media reports, Barcelona are interested in fellow defender Daniel Agger while the club has brought in Kolo Toure from Manchester City and Aly Cissokho on a season-long loan from Valencia to bolster their defensive line following the retirement of Jamie Carragher.
Rodgers said Liverpool would consider bringing in further reinforcements.
"Yeah I think it's something that we're looking at, certainly," he said.