The Reds have struggled to sixth and seventh-placed finishes in the last two campaigns, but were in sublime form following the appointment of Kenny Dalglish in January.
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Despite their great run of results, the Merseysiders had to look on as arch-enemies Manchester United won their 19th league title, moving ahead of the Anfield club in the all-time honours list in the process.
But Suarez, who scored four goals as Uruguay won the Copa America this summer, is confident that the team are heading in the right direction and that 21 years of disappointment can come to an end.
The 24-year-old said in the Daily Star Sunday: "At Liverpool we always dream about being Premier League champions.
"We know, of course, that it's a very difficult league to win and very competitive. There are a lot of teams who want to be champions.”
The return of King Kenny, coupled with the club’s ambitious new owners, have brought a renewed sense of optimism to the club, as well as an investment in new players to help Liverpool make the next step.
After signing Suarez and fellow striker Andy Carroll in January for a combined £57 million, Dalglish has splashed out a further £45 million so far this summer on midfielders Stewart Downing, Jordan Henderson and Charlie Adam, giving the squad a strength-in-depth that has been missing in recent times.
And Suarez says the combination of new signings and not having to play in Europe could be the key to success in 2011/12.
"Now we have a squad of quality. We trust our manager and we trust each other as team-mates. We are confident about that," he said.
"We have the ability and I think Liverpool certainly should be aiming to finish among the Champions League places. Then there is always that dream, a little dream, about actually winning the Premier League.
"Maybe not playing in the Europa League this year will really help us. We will be able to focus on the league and on getting as high up the table as possible."
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