Brentford have offered a club record fee of £35million for Fiorentina's Argentine winger Nicolas Gonzalez.
The Bees, who are without star striker Ivan Toney until January, have been looking for attacking reinforcements this summer in a bid to bolster Thomas Frank's squad.
Having made an initial proposal of approximately £26m earlier this month, the west London club have now tabled a £35m bid for Gonzalez in a move that would make him Brentford's most expensive ever arrival.
However, Fiorentina manager Vincenzo Italiano has cast doubt over his potential move to Brentford.
Keen to play down speculation of his exit, the head coach said on Wednesday: 'He will definitely stay with us.'
Forwards Bryan Mbeumo and Yoane Wissa have been in fine form so far this season, each netting in Brentford's 2-2 draw against Tottenham and 3-0 win at Fulham last weekend.
Brentford have been active in the transfer market this summer, signing Kevin Schade for £22m as well as former Wolves centre-back Nathan Collins for £23m.
Frank's side have also spent £11m on new goalkeeper Mark Flekken, who has replaced David Raya between the sticks following his loan move to Arsenal.
The Bees sit fourth in the table behind Brighton, Manchester City and Arsenal, who each won their opening two fixtures.