The Anfield manager was rewarded with a new long-term contract on Monday after leading Liverpool back to the Champions League with a second-place finish in the Premier League, ending a five-year absence from Europe's premier club competition.
Liverpool narrowly missed out on the league title to Manchester City, with a home defeat against Chelsea and a dramatic collapse in a 3-3 draw with Crystal Palace in the penultimate game of the season effectively ending their hopes of winning a first English top-flight crown for 24 years.
Rodgers is eager to atone for that near-miss and win the Premier League next season, however, he also has high hopes for the Merseyside club's Champions League campaign.
Liverpool have won the competition five times but are expected to enter the group stage in pot three, meaning that they will likely face a difficult assignment to qualify for the last 16.
But Rodgers is hopeful that the legendary Anfield atmosphere in continental clashes will have an impact on their fortunes.
"We're into the Champions League. Our dream and goal is to win the Premier League," Rodgers told the club's official website.
"That's what we want to do. We've shown this season that we can compete for that. With some new additions in the summer, we believe that we can fight again.
"The objective for me was to try to get Liverpool established again as one of the leading clubs in European and domestic football and we're on course for that.
"I've seen the games before and I've been fortunate enough to have been at Anfield on a Champions League occasion and they are truly special occasions.
"You see the support the players get. Throughout my time here, in the big games, the supporters really show how passionate they are and they show why they are the great set of supporters that they are.
"We'll really look forward to it. We know that, in the Champions League, if we can perform well away from home, that in the home games, we're going to be hard to beat because of the supporters and the quality of the team."
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