The Uruguayan looked likely to leave the Merseysiders during the transfer window, with the player frequently stating his desire to move to a club playing in the Champions League.
However, Suarez admits that he was content with remaining at the Reds once he realised that a move away wouldn't materialise.
"For me, it has been closed for some time," Suarez told the The Mirror. "I made the decision to stay at Liverpool some weeks ago and I want to stay and work for the team from now on.
"I will go back to Liverpool to play and I hope to be the same player the fans can trust.
"I said I wanted to play in the Champions League, but when that didn't happen, I knew I'd be happy with life to have my future at Liverpool."
Arsenal saw two bids rejected for Suarez over the summer.