The Uruguayan striker plays down talk that the Reds are one of the favourites for the Premier League crown but is pleased to have the fans' support after a "difficult" year
Brendan Rodgers' side sit just two points behind leaders Arsenal after their 5-0 hammering of Tottenham on Sunday and would move above the Gunners with a win over Cardiff City on Saturday.
But Suarez, who scored twice at White Hart Lane to take his tally to 17 goals in just 11 Premier League appearances this term, feels that upcoming trips to Manchester City and Chelsea will be major tests.
"I think it's too early to say," the Uruguayan said of his side's title hopes at the Football Supporters' Federation awards, where he was named Player of the Year.
"If we continue at this level the next two or three weeks, we can win the league or we can finish in the top four.
"It's important we concentrate and focus on the next game. We know that, after Cardiff, we have two very, very big games [at City on December 26 and Chelsea three days later]. That will be important to what comes next."
Suarez went on to express his gratitude to Liverpool fans for their reaction after his failed attempts to secure a transfer away from Anfield in the close-season.
The 26-year-old had publicly stated his desire to move to a club in the Champions League, with Arsenal having two bids rejected, but Reds supporters have him fully since his return from a 10-game ban for biting Chelsea's Branislav Ivanovic in April - a fact that he considers the highlight of a "difficult" year.
"I was able to win the supporters back and that was unbelievable when I came back to play," Suarez enthused. "They helped me and that was important for me, for my confidence, and for my family, because they are together with me in this."