Henderson suffered a repeat of his heel problems in the 1-0 win over Manchester City on New Year's Eve.
The Liverpool captain, who went to the USA to see a specialist about the injury during a long absence last season, has played in the Reds' last two league games.
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But he has also missed the FA Cup ties against Plymouth and last week's EFL Cup semi-final at Southampton.
Henderson could play on Wednesday when Saints head to Anfield for the second leg.
Liverpool midfielder Jordan Henderson is battling through a heel injury
Henderson has only played league games since injuring himself in the Man City win
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Jurgen Klopp's Liverpool face Southampton in the EFL Cup on Wednesday
And Klopp says the England international is training as he usually does.
“When the team are out running for recovery, he’s on a bike is what he does different," Klopp said.
“He always feels a little bit, but he can cope with it.”