The Hammers are also prepared to pay €4m in bonuses for the versatile defender.
Newsonline report that Aina’s Serie A club, Torino have, however, turned down the offer and wants a total of €10m for his permanent exit.
It remains to be seen whether West Ham will improve their bid before the end of Thursday’s transfer window.
The 25-year-old has reclaimed his place in Torino’s starting line-up after falling down the pecking order at the Turin-based outfit in the second half of the last campaign.
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Aina joined Torino from Chelsea in 2019 after spending the previous season on loan at the club.
He has also spent time on loan at English clubs, Hull City and Fulham.
