The Nerazzurri boss is thought to want an option to buy included in any loan deal for Giroud, who has fallen out of favour under Frank Lampard.
The 34-year-old has been restricted to a handful of appearances off the bench, playing less than 50 minutes of Premier League football for Chelsea so far this season, neither scoring nor assisting in that time.
Giroud voiced his frustration at his lack of game-time recently, telling Telefoot: "It's worrying. I thought I still had a role to play at Chelsea but my playing time is getting reduced a lot. It's going to have to change or a decision must be made."
However, given that he would be expected to fulfil a similar rotational role at Inter, and with West Ham and Tottenham also thought to be keeping tabs on the striker, Conte has had to shortlist alternatives to the Frenchman.