The Uruguayan's 31 goals almost propelled Liverpool to the Premier League title in 2013-14, before he departed for Camp Nou.
Without Suarez, Liverpool's Champions League campaign was ended in the group stage, while Barca are preparing for Wednesday's quarter-final first leg against Paris Saint-Germain in the French capital.
Asked if the desire to win the competition was behind his transfer, Suarez told Champions Matchday: "Of course. Barcelona are always a candidate to win the Champions League.
"That's a plus here, as the clubs I've played for before didn't really have the chance to win big [European] trophies - maybe a domestic league or cup.
"Playing in a team like this, where all the players want to win every match and everything, that is a sign that it's all about silverware - whether it's the Champions League, the Liga or whichever trophy's available. We have a chance of making the final."
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