The Brazilian sustained the problem during Liverpool's 2-0 Champions League win over Atletico Madrid at the beginning of November, with manager Jurgen Klopp confirming at the time that the injury was "serious".
However, Firmino was back in training with his teammates on Thursday and could now be in contention to feature during Saturday's Premier League clash with Aston Villa.
Klopp's men played seven games during Firmino's absence, winning each of the last six in a row across all competitions.
The boosts come in the midst of a packed fixture schedule for the Reds, who have already played three of their nine fixtures in December.
After welcoming club legend Steven Gerrard back to Anfield this weekend, Liverpool will then face Newcastle United, Tottenham Hotspur and Leicester City before Christmas. body check tags ::