The Denmark international has made 39 appearances in all competitions for the Reds this season, scoring four goals in the process.
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Agger has long struggled with a succession of knee and back troubles, undergoing surgery on a recurring spinal injury in 2009 and admitting on Tuesday that he had considered retirement.
The centre-back's latest treatment involves a stint of rehabilitation that could preclude him from pre-season training, although the club are yet to confirm the likely duration of his recovery.