Alonso, 25, missed six weeks with a broken metatarsal - and then suffered the same injury in his left foot during his comeback match against Arsenal 10 days ago.
Anfield medics originally expected Alonso would be back in action this week.
But the injury has shown no signs of improvement so Alonso was sent for a scan on Monday - and told he might not be fit until the end of December.
Alonso admitted: "I didn't expect to be out for more than six weeks like I have been. The relapses are a shame."