Gerrard was hurt following a tangle of legs with Fernando Torres during Sunday's 1-1 draw at Chelsea but was able to complete the match.
"I think Steven will be alright," Rodgers told the club's official website. "He has just opened up his medial ligament a bit. He has got some ice on his knee and we'll find out the full extent later on."
Luis Suarez cancelled out John Terry's opener at the Bridge to earn the Reds a point.