Strinic is entering the final year of his contract at Dnipro and the Russian club are open to offers for the full-back rather than risk losing him for nothing next season.
West Ham boss Sam Allardyce is keen to bolster his left-back options despite recently signing Aaron Cresswell from Ipswich to fill that role.
Allardyce wants to bring in Strinic to add depth to his squad so that the 26-year-old can battle Cresswell for the left-back spot in his starting XI next season.
Strinic, who has been linked with a move to England in the past, is thought to be keen on a move to the Premier League.
Strinic was named in Croatia preliminary World Cup squad for Croatia this summer, but failed to make the final 23 for the finals in Brazil.