The Reds forward is reportedly ready to tell Liverpool that he wants to leave the 18-time English champions at the end of the season.
Premier League sides Arsenal and Chelsea are being linked with a move for the 20-year-old forward, whilst Real Madrid are also potential suitors.
But former Liverpool midfielder Barnes, who has two years remaining on his current contract, believes Sterling needs a reality check.
“He is only 20 and has not achieved anything, he has not won anything,” Barnes told BBC Sport.
“The time is not right for him to move, but if he wants to move the club should sell him. If he goes to Manchester City, to give himself a chance of winning the league, he will not become a regular for them. We have seen it with players in the past like Scott Sinclair.”
Sterling has scored seven goals and has made seven assists in 35 Premier League appearances for the five-time European champions this season.
Arsenal and Chelsea are reportedly interested in signing the want-away Liverpool forward, who moved to Anfield from Queens Park Rangers under Rafael Benitez in 2010.
Sterling made his debut under former Liverpool manager Kenny Dalglish in March 2012.
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