The 22-year-old damaged the anterior cruciate knee ligament in his right knee while on international duty with Uruguay and is now set to undergo surgery.
Rodgers has also confirmed he is willing to allow defender Andre Wisdom to move out on loan.
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"He's 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 him because he's never given me a minute's problem since he's been here and this was probably the year where he needed to go out and play so unfortunately that put an end to that.
"It's something that we're looking at, a player to come in in that position. I really need to get young Andre Wisdom out on loan.
"It's one to strengthen the squad but it's also to allow some of our younger players to develop, for us to maximise Wisdom and his talent we need to get him some games and to get him out on loan, but I can only do that if somebody with a bit more experience can come in and support the ground. So it's two-fold really, but it's certainly a position that we're looking at."
Rodgers also denied reports suggesting that Liverpool had rejected a bid from Napoli for Martin Skrtel.
"I haven't been told anything about that whatsoever," he said.
"It was mentioned this morning but it was the first I'd heard of it. Ian Ayre does a terrific job and informs me straight away, but I haven't heard anything."