The striker, who signed a new contract on Friday, insists he wants to win a "big trophy" with the club, while Brendan Rodgers has backed the Uruguayan to break records.
The Uruguayan has been in sensational form at the start of the 2013-14 campaign, scoring an incredible 19 goals in 12 league games, including two more in the 3-1 victory over Cardiff City on the weekend.
That result propelled Liverpool to the top of the table and the Uruguay international is desperate for the Merseyside club to clinch the title for the first time since 1990.
"It's my dream; I hope to win the league and a big trophy with Liverpool." Suarez told LFC TV when asked about winning a title.
Manager Brendan Rodgers, meanwhile, has backed Suarez to break the goalscoring record for a single season in England's top flight, with the current record of 34 held by Andy Cole (1993-94) and Alan Shearer (1994-95).
"He looks like he can score a hat trick in every game, doesn't he? He can do, because he has got that quality. He will certainly push [the record] close," the Reds boss said. "You can put him in that bracket of world class. I think one or two of his off-field antics have maybe detracted from his performance level, but you see a different man now.
"He is mature. You see he is happy, confident and at peace with everything in his life on and off the field. Luis is just a brilliant player, a joy to work with. He gives me everything, every day of his life."