The Spain international arrived back at the club from Valencia in June 2012, winning a Liga title in his first season, having left Barca's youth system at the age of 16.
However, Alba, who scored in Spain's 2-0 FIFA World Cup qualifying win over Finland on Friday, is keen not to rest on his laurels.
"I hope to be among the best in the world by the time I finish my career," he said.
"I'm flattered that people are talking about how well I am playing, but I don't take too much notice of it because when I have a bad game it's the opposite, and people slate me endlessly, but when I have a good game it's as if I'm the best player of all time.
"I hope I can keep growing as a footballer and in many years' time be among the best in the world."
Spain's win over Finland ensured they kept up their unbeaten record in qualifying ahead of their friendly against Chile at the Stade de Geneve on Tuesday.
Vicente del Bosque's side sit three points clear of second-placed France in Group I, with just two games remaining.
