The former forward also believes his exit was handled in the wrong way.
The young forward has arguably been the biggest transfer of the summer so far, with him joining Manchester City for a big money fee that made him the most expensive English player ever.
With such a big fee, there is high expectation now on him at the Etihad, with many saying he must become a world-beater to justify such a large price tag.
Rush though, says he would have liked to see him stay at Anfield as he isn’t the finished article, although he believes he could develop into one of the best in the world.
“I’d have loved him to stay for another year and develop because he’s not the finished article,” he told 888 Sport.
“His left foot is a bit weak and he’s still got a lot to learn but he has the potential to be anything. The pressure on him now though is like the pressure Messi or Gareth Bales deal with. If he overcomes that he will develop into one of the best players in the world.”
Exit done in the wrong way
The former forward has also lamented the manner in which Sterling exited the club, saying it was done in entirely the wrong manner.
Sterling’s move came about after months of speculation about his future, with a series of talks between him and Liverpool over a new contract failing to reach a satisfactory conclusion.
An ill advised interview from the youngster with the BBC then ramped up the pressure, with him and his agent receiving heavy criticism from all angels for the way they were conducting themselves.
And Rush has wished him good luck with Manuel Pellegrini’s side, but backing Liverpool for how they went about dealing with the saga.
“I wish him good luck but it was all done in the wrong way,” he added.
“I don’t blame Raheem because he’s a young lad. It was his agent who most probably did all that. Manchester City were always going to get him in the end because of the amount of money but I think Liverpool conducted themselves in the right way.”