The Hammers are also finalising a deal for Gil Vicente centre-forward Pablo.
The London Evening Standard says West Ham are pushing to sign both attackers in the coming days.
West Ham are allowing centre-forward Niclas Fullkrug to leave on-loan for AC Milan and also Brazilian winger Luis Guilherme.
Castellanos, meanwhile, was on the books of City Football Group and played for New York City FC before leaving MLS for Lazio.
Related：
West Ham United
Milan
Lazio
Gil Vicente
Füllkrug
Taty Castellanos
Pablo