Reports had suggested that Gerrard would be out for four weeks following his operation.
That scenario would see him miss Premier League games against Sunderland, West Bromwich Albion and Manchester City.
Dalglish's best hope will be to have Gerrard available for the season run-in. The Liverpool boss is already without 19-year-old midfielder Jonjo Shelvey, who was ruled out for three months with a knee tendon injury in February.
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