West Ham were reportedly said to be keen on Kalinic last month.
Spanish outlet El Desmarque claim West Ham are keen on the 30-year-old striker, who joined AC Milan last summer on a loan deal with an obligation to make the move a permanent one this summer.
That means the 42-time international is now officially a Milan player, but he looks set to leave as immediately as he has joined - especially after Sky Italy journalist Gianluca Di Marzio's latest claim.
The well-renowned transfer expert claimed on his official website that Spanish giants Sevilla and Atletico Madrid have both enquired after the former Blackburn Rovers striker ahead of a potential switch to Spain.
Kalinic struggled to hit the heights expected of him when he joined Milan from Fiorentina, managing just six goals and six assists in 41 league and cup appearances - though 18 of those were substitute appearances.
West Ham must move quickly if they indeed intent on bringing Kalinic back to the Premier League, after he scored seven goals in 44 appearances in England's top flight for Blackburn.