The 25-year-old is Brentford’s primary target to strengthen in attack after striker Ivan Toney was suspended until January for breaching the FA’s betting rules.
Fiorentina are expected to reject the latest approach after manager Vincenzo Italiano played down a summer move on Wednesday. He said: “He will definitely stay with us.”
Thomas Frank has already seen a £25.6m bid rejected for the Argentina international earlier this month.
Gonzalez has earned 24 caps for his country and contributed 14 goals and five assists during 42 Fiorentina appearances last season.
Frank’s side have started well this season drawing 2-2 with Tottenham before beating Fulham 3-0 at Craven Cottage. They next face welcome Crystal Palace to the Gtech Community Stadium on Saturday.
They have signed defender Nathan Collins and goalkeeper Mark Flekken this summer.