The Frenchman wants to leave Stamford Bridge, as he is no longer a first team regular under Frank Lampard.
He is down the pecking order, behind the likes of Timo Werner and Tammy Abraham.
Tuttosport claims Antonio Conte likes Giroud and wants to bring him to Italy.
He would be a backup for Romelu Lukaku, which makes the transfer somewhat unusual.
Giroud has expressed his desire to leave Chelsea, but for regular football.
It remains to be seen whether he chooses Inter, or a slightly less prestigious team where he could play more.