Bacca joined Milan from Sevilla 12 months ago for a fee of around £22million after his release clause was activated and is contracted to the Italian giants until 2019.
The 33-time capped international starred for the Italian giants last season where he scored 20 goals in 43 appearances in all competitions.
Should a fee of above £15.5million be agreed, it would beat West Ham’s transfer record, which is for the purchase of Andy Carroll from Liverpool three years ago.
In other West Ham transfer news, Crystal Palace have joined the race to sign £15million-rated striker Diafra Sakho.