Liverpool have struggled in his absence, picking up just one point from a run of games that included a 0-0 draw with Arsenal, a 3-0 defeat by West Ham United and Saturday's 3-1 loss to Manchester United.
The 25-year-old Henderson would visit orthopaedic surgeon Dr James Cozzarelli for treatment, although he was not expected to require surgery, the reports said.
Liverpool were hopeful that Henderson would feature after the international break at the start of September but are now resigned to losing him for longer than anticipated.
However, midfielder Adam Lallana, who missed the club's last three games with a thigh injury, has returned to training and is in contention to face Norwich City in the Premier League on Sunday.
Phillpe Coutinho, who was suspended for the game against United, will likely return to the starting line-up when Liverpool travel to France to face Bordeaux in the Europa League on Thursday.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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