The Brazilian playmaker underwent a scan today after suffering the blow during the Reds' 2-0 victory over Sunderland at Anfield on Saturday.
Coutinho was stretchered off around the half-hour mark of the encounter after his foot was caught by Didier Ndong during a tussle for the ball.
There has been no official confirmation from the club, but the Daily Mail reports that the 24-year-old will be ruled out until the New Year.
As a result of the injury, Coutinho is expected to miss matches against Bournemouth, West Ham United, Middlesbrough, Everton, Stoke City, Manchester City and Sunderland, as well as the FA Cup third round.
The attacker, who has scored six goals in all competitions so far this season, has helped the Reds to second in the Premier League table after 13 games.