Liverpool finished sixth after an impressive second half of the season when Roy Hodgson was replaced by Anfield legend Dalglish.
And now Suarez, who has quickly become a fans favourite, believes they can match Chelsea and Manchester United a the top of the table.
Instant hit: Luis Suarez showed his promise after moving to Liverpool in January
'I think the form we have showed over the second half of the season bodes well.' the Uruguay international told LFC Weekly. 'We've been playing well and I think we've been getting into the type of form that we know we'll have to keep up for a whole season if we want to be title contenders.
'This is something we're optimistic about for next season and if we can hit the ground running and maintain the good form then I think we've got a good chance of doing well.'Suarez did not win a league title during his three and a half years at Ajax and had to watch from afar as they clinched the Eredivisie in May.
Leading the way: Kenny Dalglish's appointment as manager heralded a change in fortunes for the Anfield club
But the 24-year-old earned a championship medal having scored seven goals in his 13 appearances for the Dutch giants.But he added: 'I did get a medal but I'd be the first person to say that the league title was down to the rest of the team and Frank de Boer, the manager.'It's fair to say I took part and played a few games but I would like to have played in more games to really feel I deserved a medal. The credit there goes to the squad and to the first team.'
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