The former Reds star has been released from his contract at Chelsea and is currently a free agent.
Carragher wrote for the Telegraph: "There was a sense that Sterling never quite won the love of others.
"I am not sure how high he would feature on an all-time list of the greatest England and Manchester City players. My suspicion is that he would rank lower than he should.
"Had Sterling’s career ended with his Manchester City exit four years ago, he would have already achieved more by the age of 27 than most manage in a lifetime.
"Instead, he looks like another example of a player who, while reaping substantial financial rewards for his talent, is a victim of a recurring football problem where those who shine brightest in their youth must wrestle with the perils of being overplayed, compromising their chance to prolong a career at Champions League and international level."