Whether or not that is the case, there has been a bigger, more significant problem: a succession of Chelsea managers have failed to pick him. It was a bold move in the first place, running down his contract at Manchester City just as the club looked to be in a position to mount a serious challenge in English football.
At his first Chelsea press conference he said his England U-21 team-mate Scott Sinclair had convinced him it would be the ideal club. It was pointed out to him that Sinclair had tried in vain for a number of years to break into the Chelsea first team.
Now on his way to Liverpool for £12m, it is the turn of Brendan Rodgers to get the most out of a talented player. There have been many mercurial stars whose form has inexplicably gone up and down – the question is whether Sturridge, still only 23, is quite good enough to be indulged in spite of those fluctuations.
He came to Chelsea promising to make an impact on the team and will leave having made 96 appearances, 47 of them as a substitute. He spent the second half of the 2010-11 season on loan at Bolton Wanderers, where he hit a run of goalscoring form that put Fernando Torres' struggles into perspective with him having joined from Liverpool in the same month that Sturridge was shipped out.
The arrival of Torres was unfortunate for Sturridge, denying him the opportunity to play in the more central role that he claims is his most natural position. Yet even if Torres had never joined, you have to wonder whether Sturridge would have been Didier Drogba's natural successor.
Sturridge's goals record of 24 for the club is not an embarrassment. Torres has scored exactly the same amount for the club having made more starts (69).
The problem at Chelsea is there is a time limit on every player to make an impact. Once that runs out, you are surplus to requirements.
Chelsea will not have made the decision to sell lightly, given how young he is and the prospect that he could improve. As ever, the signs point towards a major signing next month, with Radamel Falcao at the top of the list. Even Chelsea, with Roman Abramovich's investment, have to show that they can make money as well as spend it in the transfer market. Sturridge, with his youth, is a particularly saleable asset.
With four caps, all off the bench, his England career has never really taken off either. He was one of the standby players for Euro 2012 and was not taken by Roy Hodgson, even when Wayne Rooney was suspended for the first two games.
He finally played for the new England manager in the defeat to Sweden in November.
At Liverpool, he will hope to start matches but would still arrive beneath Luis Suarez in the pecking order. It is a situation with which he is familiar – whether he is capable of changing it remains to be seen. (© Independent News Service)