The 32-year-old was stretchered off the pitch during the club's Capital One Cup clash with Notts County on Tuesday, with the Reds clinching a 4-2 victory in extra time.
But Rodgers is relieved by the progress made by the Ivory Coast international and revealed that the defender is in contention to face Manchester United on Sunday.
"His injury is nowhere near as bad as what we thought. We'll just assess that over the next 24 to 48 hours," Rodgers told reporters on Friday.
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"If it's not this weekend, then we would think that after the international break he will not be too far away."
The Anfield outfit also saw duo Joe Allen and Aly Cissokho leave the pitch with a hamstring and ankle injury respectively, with the on-loan defender facing up to six weeks on the sidelines.
"With Joe, likewise, it was only a grade one strain, so he may be doubtful for the weekend but, certainly after the international break, he'll be fine," Rodgers explained.
"Cissokho will be slightly different. He could be out for four to six weeks, which is a blow because he came in and trained really well last week. He's on crutches at the moment and we'll just look at that over the coming weeks but he certainly won't be available [to face United]."