Inter drop out of Kily race
The Italian giants are unwilling to meet Valencia's asking price for the player which is believed to be in the region of £17 million.
The 27-year-old is expected to leave La Mestalla this summer and Inter and Barca were leading the chase to sign him.
Inter are looking to bring in a left-sided midfielder and had hoped to team Gonzalez up with his former Valencia boss Hector Cuper at Giuseppe Meazza.
Inter president Massimo Moratti admitted unless the Spanish champions lower their asking price of Gonzalez they will look elsewhere.
As far as I'm concerned, under these circumstances, the negotiations are over. Valencia are simply asking for a fee that is too high," said Moratti.
New Barcelona boss Louis Van Gaal has revealed he is hoping to bring Gonzalez and his former Valencia team-mate to Camp Nou.
"I also want someone on the left of midfield who can improve our style of play. That's why we have to sign players like Mendieta and Kily," said Van Gaal.