The Al Ettifaq coach feels Jones is capable of driving the Reds midfield over the long-term.
"I have just known all along that with the right guidance and support he can become that Scouse heartbeat of the team," Gerrard, who coached Jones with the Reds youth team, told The Times. "And I think he is ready to be that heartbeat now.
"He was a typical young kid coming through. Very technically gifted, very skilful, tight control. He could run, he still had a bit of growth to come.
"The key thing for me with all the kids of that age is have they got that hunger and that drive? Are they prepared to make sacrifices in order to be consistent?
"Curtis still has a lot to learn, a lot of evolving to do. I am really excited to see how Arne Slot can take him onto that next level. He is still young.
"Rafa (Benitez) had to grab me to take me to another level, and the exciting thing for me looking in is that Arne seems the man who can really get Curtis to the next level.
"If he can get him there we will have a top, top international player on our hands."