The Italian is set to act as cover during Aaron Cresswell's injury absence.
The Italian international, who can play at left or right back comfortably, is currently playing for Inter Milan.
Ex- Newcastle United man Davide Santon
However, ESPN report that the player wants the move to West Ham and is in London for a medical.
The deal is expected to be a season-long loan deal with a view to a £5 million permanent deal should he impress during his stint at the Olympic Stadium.
Aaron Cresswell celebrates scoring the second goal for West Ham
West Ham have been looking for a new left-back all summer but the search was recently intensified with the injury suffered by their only natural left-back on the books, Aaron Cresswell.
In his absence Sam Byram played out of position on the left but struggled in the Europa League first-leg v NK Domzale and that again hastened West Ham’s search.
West Ham's Sam Byram receives instructions
Santon, who has eight caps for the Italian national team, spent four years at Newcastle before returning to Inter Milan in 2015.
The 25-year-old looks like he is on his way back to the Premier League.