You are guessing Stan. Look at the work he has put in to regain fitness in America. The lad has worked tirelessly for months. It is well known that players in Italy have a similar cautious approach to injuries and still have some of the best teams and international football in the game. He can't be relied upon but it would be ridiculous to try and offload him on the cheap.
I don't think the problem is with his efforts to get back to fitness but with how he reacts to little niggles. Some players carry on through the pain, which goes away if it isn't a problem, but Sturridge seems to buckle the moment he feels the slightest twinge.