The Uruguay international was named player of the tournament in South America at the weekend after helping his country to win their continental championship for a record 15th time.
Suarez, 24, is now taking a well-earned break but Liverpool are optimistic his exertions in the Copa America will not impact too heavily on their start to the Barclays Premier League campaign, which kicks off in 18 days' time.
Champion: Luis Suarez kisses the Copa America trophy
The player has already made a significant impression at Anfield since joining from Ajax for ?22.8million in January, a purchase which is looking increasingly shrewd considering Suarez's form from last summer's World Cup onwards.
But having tasted international success the striker is keen to make a telling contribution at club level.
'When you play for a club like Liverpool, one of the biggest clubs in England, you've always got to have the aspiration of winning the title,' he is quoted as saying in the Liverpool Echo.
'You've got to believe with the quality we've got at this club that this can be a realistic possibility.
Star man: Suarez scored in the final
'But we know there is a lot of competition and there are a lot of other teams with the same objective.
'The next objective is to make sure you're in the Champions League places.
'We've got to have the confidence that we've got the type of quality here to be aiming for those things.
'We've got to have an excellent pre-season, prepare really well and then it's a case of being consistent through the season and have a good run of form - not just in flashes through the season.'
Premier ambition: Suarez believes Liverpool can win the title
Suarez certainly showed in the first five months of his Reds career that there is hope for the future.
However, he himself pointed to the leadership of Kenny Dalglish, who replaced Roy Hodgson as manager in January and turned around the fortunes of the side, as being the key factor.
'I knew he was a significant figure in the history of Liverpool but now I know the manager is a very important person,' added Suarez.
'He has given me the opportunity to express myself and show what I can do.
'The biggest thing is the trust he puts in his players. He trusts us 100% and that makes you want to return that trust and pay it back.
Trust: Suarez has faith in manager Kenny Dalglish (centre)
'We know he's had a long career in football, so we trust in his experience, we value his expertise.'
Reports in Portugal are linking Liverpool with Porto's Uruguayan left-back Alvaro Pereira.
Dalglish is on the look-out for someone to fill the hole on the left side of defence - right-back Glen Johnson played a significant amount of games there in the second half of last season - but missed out on Arsenal's Gael Clichy while he has not followed up long-standing interest in Newcastle's Jose Enrique.
However, Pereira has a reported ?17.5million buy-out clause in his contract and with Liverpool having already spent upwards of ?42million and still to offload a number of fringe players that price may be too high.
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