The 33-year-old is out of favour at the Serie A club and is set to leave for around £9 million when the winter transfer window opens.
Juventus director of football Fabio Paratici have travelled to London to discuss the player’s potential transfer, and the likes of Manchester United and Tottenham Hotspur have also been linked with an interest.
West Ham could do with a veteran striker in the mould of Mandzukic given their recent struggles in front of goal.
Manuel Pellegrini’s side have only managed to score 14 Premier League goals thus far, and will need to improve significantly in the final third during the second-half of the campaign to boost their top-seven chances.
The Hammers brought in Sébastien Haller for a club-record £45 million in the summer, and while the Frenchman has scored four goals in 11 games, his cover Albian Ajeti has struggled to impress.
With six league titles (four with Juve and two with Bayern Munich) and 212 career goals to his name, Mandzukic brings a lot of experience to the table, and he could be a quality cover and competition for Haller despite being 33 years of age.