The youngster made a big money move to Manchester City from Liverpool last summer, citing his need to win medals as the cause of the transfer.
After an initially bright start though, he has struggled to impress, with just six goals in the Premier League to his name so far.
Indeed, it has been a poor season for his new team in general, with them now far out of the title race and fighting just to make sure they finish in the top four.
That is not what Sterling signed up for, and Barnes says it should be an example to both Kane and Barkley, who have both been the subjects of rumours about their future.
“I always say that young players who have one good season should stay at their club for four or five years,” he told Goal.
“Until you show a four of five years of consistent quality, all you are is potential. I said for Raheem’s sake he should have stayed at Liverpool to improve.”
“He’s gone to Manchester City and you can see what’s happened. That is why Ross Barkley should stay at Everton and Harry Kane at Tottenham, stay there to prove you can do it and then move to what you consider a bigger club.”
Whether both players stay at their clubs could be determined by how they fare at Euro 2016 in the summer.
If both shine at the tournament, that could put both at the top of big teams’ shopping lists in the summer and force their current clubs into selling, just as Liverpool were with Sterling.
Given the form they have enjoyed this season though, there is no denying where is best for them at present.