The Brazil international has not played for the Premier League club since August 26 after suffering the injury in the warm-up to their game against Manchester City.
The 25-year-old holding midfielder, who missed six months of last season with a knee injury, played for the club's under-21 team last week and will now come into contention for Saturday's home clash with Southampton.
"Lucas Leiva will return to the squad, which is great news because he's been working very, very hard and played the reserve game last week," Rodgers said on the club website.
"He's very much looking forward to it. He's worked tirelessly in his recovery. We're just trying to nudge him along and make sure it's the right time. Mentally he's a tough boy.
"It's a big boost because he's well in tune with what we're trying to do here. He's been kicking his heels on the side wanting to help his mates and the group, so I am delighted to have him back."
Lucas' return could free up Steven Gerrard to play a more attacking role.
The Liverpool captain's swashbuckling instincts have been curtailed this season as he has adopted a more cautious approach playing a holding role alongside close-season recruit Joe Allen.
Rodgers denied changing Gerrard's role within the team after the midfielder was again subdued in the 2-1 defeat to Tottenham Hotspur on Wednesday.
"I don't think there has been a clear change in his game in terms of what I have asked him to do," the Liverpool manager said.
"Steven has always been the player who makes the difference over the years and, OK, he may not have had the goals this season that he has wanted but he has still been effective. There has been nothing more or less I have asked in terms of defensive responsibilities.
"He has had to take on more of a mantel because it is a much younger group. In the past he has played in teams with more experience around him and I think that is the biggest change this year."
