Brendan Rodgers' men find themselves second in the Premier League after 11 games, their only defeats having come at the hands of leaders Arsenal and third-placed Southampton.
Liverpool also went into the international break on a high following a 4-0 victory over Fulham.
Although Aspas has not had the impact he would have liked thus far, partially due to a torn thigh muscle he sustained in October, the Spaniard has delivered an upbeat assessment of the club's form.
"I think we should be aiming to finish in the top four - I think it is the minimum for this club," he told Liverpool's official website.
"The squad is very good; you can see that when you consider it player by player.
"My ambition is to play as many times as possible and to try to do it in the best possible way to finish in the top four."
Liverpool face Merseyside rivals Everton, who have lost just one league game so far this season, on Saturday.
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