The 19-year-old has been lined up to fill the boots vacated by Daniel Sturridge as the team's third-choice centre-forward after Roberto Firmino and Divock Origi, who has just signed a new contract.
However, Klopp wants the player to start developing his all-round game.
"I love the boy, he is fantastic player, but one of the goals I would have scored," said the manager.
"One hundred percent (it is a big season) but it depends on him as well," Klopp added. "Divock Origi stays, which is good news, Bobby Firmino is still there.
"Rhian Brewster is a top striker, he is a top talent and I have told him already that he has an important role this year but how important depends on him.
"We will see. He has to play different positions as well -- the centre, wing is possible I think. We will see how we line up, but there will be opportunities for him, I am sure."
European champions Liverpool have so far signed Dutch youngster Sepp van den Berg but are not expected to make any major signings in the transfer window.
"Rhian Brewster, (Alex) Oxlade-Chamberlain didn't play last year, all the young boys didn't play for us last year," said Klopp.
"The transfer market is open. We will see what we do, but I don't think it will be the biggest transfer window of all time."
In addition to Brewster's double there were also goals for Origi, Curtis Jones, Bobby Duncan and Nathaniel Clyne in a squad that relied heavily on youth, with a number of internationals still to return to training.