Ahn missed a penalty during the first half of Korea's 2-1 win over Italy on Tuesday, but was hailed as a national hero when his 116th-minute header set up a quarter-final with Spain.
Gaucci told Italian sports daily La Gazzetta dello Sport: "That gentleman will never set foot in Perugia again.
"He was a phenomenon only when he played against Italy.
"I am a nationalist and I regard such behaviour not only as an affront to Italian pride but also an offence to a country which two years ago opened its doors to him.
"I have no intention of paying a salary to someone who has ruined Italian soccer."
However, Perugia coach Serse Cosmi added another twist to the tale by declaring he would like Ahn to stay at the club and urged Gaucci to reconsider.
"I consider him a player with enormous potential," Cosmi said. "I wouldn't have any objection at all if the club decided to extend his contract for next season."
Fifa, meanwhile, refused to "interfere" with the decision to dismiss Ahn.
"It's between the player and the club," Fifa communications director Keith Cooper said.
"It's not for us to interfere. No-one has complained to us."
Ahn Jung-Hwan joined Perugia on loan from the South Korean team Pusan Icons in the summer of 2000, but he scored just five goals in 29 appearances.
Even before scoring his famous goal, Ahn, with his model looks, was a huge celebrity, the closest thing the Koreans have to David Beckham.
He is married to a former Miss Korea, Lee Hye-Won.