The 34-year-old has grown tired of his bit part role with the Stamford Bridge club.
He wants regular football and will look to move in January.
According to Tuttosport, both Inter and Juve want Giroud as they see him as someone who can offer a lot of versatility within the squad.
Inter want him on a six month loan with a view to a permanent deal in the summer.
Il Bianco Nero also claims Juve want Giroud, as they see him as someone who can come in and score goals when Cristiano Ronaldo is rested.
The issue for Giroud is that both clubs would have him as a squad option, not as a starter, which is the role he currently plays at Chelsea.