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The 21-year-old struggled to break into the first team under former boss Brendan Rodgers but scored 10 goals under manager Jurgen Klopp since the German took over in October.
Origi, who scored the opening goal in Liverpool's friendly win over AC Milan on Sunday, will face competition from Daniel Sturridge, Christian Benteke and Danny Ings for a spot in the first team.
"It can be (a big season for me). I still have to work a lot and there's a lot of room for improvement, but I try to learn day to day and we're learning as a team also," Origi told the club's website.
"The most important thing is to make steps and last year I had some good moments, so I want to learn and become more consistent to help the team even more and become an important player in the team."
Midfielder Jordan Henderson has also backed Origi to make his mark in the upcoming season.
"Since he's come into the club he has progressed throughout his time here and he is getting better and better," Henderson said.
"I thought he finished last season brilliantly and then got a bad injury, but he is looking sharp in pre-season again and I think he is going to have a big season because he is a big player for us."
Liverpool, who finished eighth in the Premier League last season, will start their new campaign with a trip to Arsenal on August 14.
