Bacca, who scored a hat-trick for Milan against Torino at the weekend, was the subject of a £20million approach from the Hammers earlier this month
West Ham manager Slaven Bilic needs another striker following two high-profile injuries
The Hammers' revised offer will give Milan more cash up front but with the total sum ultimately falling below the approach made earlier this month.
A move from Serie A to the English top-flight would double Bacca's wages from the £60,000 per week he earns at the San Siro to £120,000 in London.
The 29-year-old has already been involved in discussions regarding a potential move away from the Rossoneri but recently revealed his reasons for choosing to stay in Italy.
'When the intermediary presented the offer, I consulted with my family and decided to stay, it was the right thing for me to do,' he told Sky Italia, without mentioning West Ham directly.
Andy Carroll is out for six weeks after injuring his knee against Astra Giurgiu
Andre Ayew has been ruled out for four months with a thigh problem sustained at Chelsea
'I wanted to remain because I promised I'd take Milan back into Europe.'
West Ham beat Bournemouth 1-0 on Sunday to register their first points of the new campaign but Bilic is already counting the cost of the Premier League's early exchanges.
Ayew will be out of action for four months after limping out of the 2-1 defeat by Chelsea with a thigh problem and Carroll could be sidelined for as long as six weeks with a knee injury.
The England international picked up the knock during the Hammers' 1-1 draw at Romanian champions Astra Giurgiu in a Europa League play-off on Thursday.
Bacca has recently revealed he turned down a move
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