During his time with River Plate he had a six-month unsuccessful loan spell at J1 League side Avispa Fukuoka.

He formed an effective striking partnership with fellow Argentine Christian Giménez and the team were placed relatively high in the league.

[4] He scored his first goal for his new team in the away game in the Espenmoos on 27 July, it was the equaliser as Basel played a 1–1 draw with St.

They ended this in second position behind Valencia, but ahead of Liverpool and Spartak Moscow to advance to the second group stage.

[6] Basel ended their league season as runners-up, but in the cup they advanced to the final and here they beat Xamax 6–0 to defend the title.

But with two victories, 2–1 away against Ferencvárosi TC and 1–0 at home against Feyenoord, saw Basel rise to third place in the group table and advance to the knock-out stage.

In the round of 32 in the 2004–05 UEFA Cup, a home game in the St. Jakob-Park on 17 February 2005, Basel played a goalless draw against Lille OSC, but the return leg were defeated 2–0 and were eliminated.

[10] Basel completed all the 2004–05 Super League season's seventeen home games undefeated, winning thirteen and drawing four.

[12] Subsequently, Basel dropped into the 2005–06 UEFA Cup, where against NK Široki Brijeg in the first round, they sealed a 6–0 aggregate win to qualify for the Group stage.

[13] In 2006, Rossi moved to France's Ligue 1 to play for FC Nantes, but when the club were relegated in 2007, he was released on a free transfer.