The 71-year-old has stated that the Anfield outfit should have moved quicker to secure the star’s future.
The England international made his desire to leave Anfield clear at the turn of the year, with the Etihad Stadium outfit splurging a cool £49 million on the versatile attacker over the summer.
Sterling’s behaviour in trying to engineer a move away from the Merseyside has led him to be the subject of hate from some of the Kop, with the youngster sure to get a frosty reception upon his return to Anfield in City colours later in the season.
Despite this, Lee has stated that Brendan Rodgers’ men should have moved quicker to secure Sterling’s services and did not treat his contract situation with enough urgency because he was a youth academy graduate.
“You would have thought when he got back that Liverpool would want to get him on a big contract but instead they seemed to do nothing and carry on with the £25,000-a-week contract he already had,” Lee told The Daily Mail.
“What world were they living in? It wasn't the going rate for one of the best players in the England team.
“Either they were trying to sell him or they were taking him for granted. It can happen when you are a young player who has come up through the youth team and reserves. You can be mucked about.
“I can relate to it. Early in my career I was top scorer at Bolton for five seasons but because I was a local boy, I was never one of the best-paid players. By the time my contract was up, they offered me five times my basic wages but it was too late for me.”
Sterling put in an impressive display in his competitive City debut against West Brom on Monday night and is set to face Chelsea later today in his first outing at the Etihad Stadium.
Lee feels the Englishman will play an important role in Manuel Pellegrini’s men’s chances of success this season.
“He can be a big star at this club,” Lee continued. “He is a bloody good footballer and a lot of people don't realise he's a tough little player as well.
“When he gets a balanced role at City, I think he will be outstanding.”
City have high ambitions for the season and will want to beat Chelsea today to make a big statement in the early days of the campaign.
Sterling’s performances are sure to scrutinised highly due to his extortionate transfer fee, with the youngster under a lot of pressure.