The 19-year-old, who scored twice in a 6-0 pre-season friendly against Tranmere, could end up saving the Reds boss millions in the transfer window if he fulfils his potential.
He 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 Klopp.
"We knew Rhian was a good player before. Why should I play it down? I just don't want to talk after a game about the guy who scored two goals.
"I saw a really good game and Rhian is a fantastic player.
"One hundred per cent [it is a big season] but it depends on him as well. 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."
Liverpool have so far signed youngster Sepp Van Den Berg but are not expected to make any major signings this summer.
"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 which relied heavily on youth, with a number of internationals still to return to training.
Of the squad which won the Champions League 40 days ago, James Milner, Adam Lallana, Simon Mignolet, Joe Gomez, Oxlade-Chamberlain, Fabinho, Origi and Joel Matip all featured for 45 minutes at Prenton Park.
