Sterling, 20, has rejected a £100,000-a-week contract and is expected to tell club boss Brendan Rodgers he wants to leave Anfield in the summer.
Manchester City are linked with the England player, but Barnes says he would “not become a regular for them”.
“Raheem has not achieved anything, he has not won anything,” said Barnes.
“Does anyone believe that if he goes to Manchester City he will be the first name on the team sheet or are they just signing him because they need English players?”
Barnes said there were other examples of players whose careers had not progressed at City.
“We have seen it with players in the past like Scott Sinclair,” he added.
Sterling, whose current contract is worth £35,000 a week, said in a BBC interview in April that he “talks about winning trophies” rather than money.
His current deal ends in 2017 and last month he confirmed that he had turned down the offer of a new contract.
Rodgers, Sterling and Liverpool chief executive Ian Ayre are scheduled to hold a meeting on Friday.
“Raheem has great potential, but Liverpool gave him an opportunity and he should stay for a couple of years,” added Barnes in an interview on BBC Radio 5 live.
“The time is not right for him to move, but if he wants to move the club should sell him. The manager cannot keep an unhappy player.
“This idea of leaving one huge club to join another huge club does not sit well with me, but it is a modern era where the power is in the players’ hands.”
Former Liverpool defender Jamie Carragher, who played 737 times for the Reds, has expressed his anger at Sterling’s actions.
“For a 20-year-old kid to be taking on Liverpool Football Club over a contract – to the pit of my stomach that just winds me up, it angers me,” said Carragher on Sky Sports. — BBC
“If it’s about trophies, Liverpool had a chance for a trophy this year – in the FA Cup semi-final at Wembley against Aston Villa. — BBC