The Uruguay defender picked up a serious knee problem while representing his country on international duty, and Rodgers admitted the arrival of another defender before September 2 was a priority.
Rodgers was also keen to allow Andre Wisdom, 20, out on loan to gain experience before the setback to Coates and said: "I feel for big Seba because he's obviously played the latter part of the game and picked up a similar injury to what Martin Skrtel had last year.
"It's probably going to rule him out for most of the season, which is disappointing for him.
"He's never given me a minute's problem since he's been here and this was probably a year where he needed to go out and play. Unfortunately that will put an end to that.
"It's something that we're looking at, certainly, a player to come in in that position. It's to strengthen the squad but also to allow some of our younger players to develop.
"For us to maximise Andre Wisdom and his talent, I need to get him some games.
"The idea is to get him out on loan; but I can only do that if we bring in someone with a bit more experience to come in and support the group. It's two-fold really. It's certainly a position we're looking at."