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Andy Carroll's commitment and effort in training has been called into question previously, and if it remains anything less than 100 percent, then no Liverpool supporter would have sympathy with the forward or reservations about showing him the door.
But Carroll himself last season stated that he was working much harder, and that his end-of-season impressive form was in part down to that.
Rodgers is an astute and tactical, but more importantly, hands-on coach, and he should relish the challenge of getting one of potentially the most dangerous strikers in the league up to the correct level of performance on a regular basis.
At 23 years of age, Carroll is still young enough to take on board the right coaching to make him a better player, particularly with regards to his off-the-ball movement.
If Rodgers has such severe doubts about Carroll's ability to perform over the long term and already has in mind the players he wants, then—providing Liverpool get an acceptable offer—it's understandable if the manager wants to cash in, cut the club's losses and move on.
With Liverpool rebuilding, it makes sense to try and do as much of the necessary culling in "Year Zero," rather than hoping for better and delaying the inevitable, especially if he has no intentions of making Carroll a regular starter.
But the former Newcastle striker still has a great chance of becoming a very, very good forward for club and country—and Liverpool should take any opportunity they have to help him on his way while he remains at the club, and in so doing, reap the rewards for themselves.