The 22 year-old is one of the rising stars of Mexican football.
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ESPN says Barca have been following Gonzalez for over 12 months and are now firming up their interest.
Indeed, it's claimed Barca sports chief Deco has spoken with the player about a summer move to Spain.
Chivas have fielded enquiries from several major European clubs, though Barca's interest has turned the head of Gonzalez.
The striker has struck a stunning 17 goals in 24 games for Chivas this term.