Asper was the first choice goalkeeper for Mjällby AIF in four seasons before signing to the Allsvenskan side AIK in 1998. Lee Baxter began the 1998 season as the first choice. But after seven games AIK had only managed to collect seven points, including only one win. On the 8 of June, Asper made his debut against Östers IF putting Lee Baxter on the bench, which would last for the rest of the season. With Asper in the net, AIK did not lose a single game in the 1998 season and they also won Allsvenskan the same year.
His performances in AIK attracted interest from Spanish club Real Sociedad, who bought him just before the 2000-01 season. However, he did not had much of a success in Spain and eventually returned to Sweden and Malmö FF in 2002, after being on loan to Beşiktaş J.K.. He won the Swedish championship with Malmö FF in 2004.