In June 1993, Tøfting moved from AGF to German team Hamburger SV (HSV) in a transfer deal worth DEM 500,000. He took part in HSV's first three games of the 1993–94 Bundesliga season, before a knee injury side-lined him. He returned to the team in December 1993, but had a hard time forcing his way into the first team due to league restrictions on the number of foreign players in the starting line-up. He was loaned out to Danish club Odense BK, playing 12 games in the last half of the 1993–94 Superliga season as Odense finished in fourth place. He was loaned out to AGF in the first half of the 1994–95 Superliga season, before returning to HSV in winter 1994. He played a further three games for HSV as a substitute, before he was once again loaned out to AGF in April 1995.