Suarez expressed a desire to leave Anfield in the close-season for a side playing in the UEFA Champions League, with Premier League rivals Arsenal seeing an approach for the Uruguayan knocked back.
However, the former Ajax man has since committed his future to Liverpool, penning a new long-term contract.
The 27-year-old is enjoying a magnificent season, his 23 goals helping put Brendan Rodgers' side on course for a place in next season's Champions League.
Although Suarez is unsure of Liverpool's title credentials, he is confident he can win silverware with the club, who currently sit fourth in the top-flight, just four points behind leaders Chelsea.
"We have 12 games left and let's see what we can achieve," Suarez told the Liverpool Echo.
"Can we win the title? I'm not sure. I think this season the Premier League is so difficult. Every team can lose games. Man City, Chelsea and Arsenal have been dropping points.
"We are very strong at home and we must keep going like this. We must just focus on every game. In football you never know what can happen.
"To be in the Champions League is what we all want. This is our objective – to play in it next season.
"We have a very good team playing at a good level and we believe we can get in the Champions League.
"I watched the games on TV this week and when you hear that Champions League music that's motivation in itself.
"I want to be there with Liverpool. It's an unbelievable competition. It's where we want to be – playing against the top teams in Europe.
"Stevie (Gerrard) has told me about Champions League nights at Anfield. He said when you have played Champions League football at Anfield you will never forget it. I want to try it for myself.
"When I arrived here I said it was my dream to play for Liverpool and play Champions League here. I know I can achieve my dreams here."
