The Marseille man, who reportedly turned down the Hammers last year, was also the subject of interest from Liverpool last January but the Ligue 1 side refused to sell their centre-back.
Negotiations are now currently underway for the Croatia international, with West Ham readying an offer of €14m (£11.8,m) which could rise to €17m (£14.4m) including bonuses. Marseille, who paid €19m (£16.1m) for the defender back in 2018, are looking to obtain a fee of at least €20m (£16.95m)
Other clubs are said to also be in the mix for the 24-year-old, who is under contract for another two years.
The Hammers are said to be in advanced talks to sign Nikola Milenkovic and are still hopeful of agreeing a fee with La Viola after stepping up their pursuit of the Serbian international.