The move is also a stretch for the Ligue 1 side due to Giroud's wages and they would hope to see the Blues pay some of them or see him lower his demands.
Inter are similarly hoping for a cut-price deal but have significantly more financial clout than their market rivals with more clubs expected to come in for the striker across January.
Giroud is interested in a reunion with Conte at Inter, although there are some concerns whether he would fall into similar problems than those at Stamford Bridge with Romelu Lukaku and Lautaro Martinez already top performers at the club.
The France manager has called on Giroud to leave Chelsea after making just one start since August which came against West Ham at home in a 1-0 defeat.
Conte's interest in Chelsea's wantaway stars extends to Marcos Alonso, who he worked well with during his time at Stamford Bridge.
Again, Inter will be stretching themselves to put up the financial package to please both Alonso, who is on £100,000-a-week and is one of the higher earners in west London, and Chelsea who will want a good fee for their full-back.
Alonso has grown unhappy at Stamford Bridge after being dropped by manager Frank Lampard since he was substituted in the first half of the 4-4 home draw against Ajax on November 5.
Furthermore, Inter would need to shift one of their current left-backs, Cristiano Biraghi or Kwadwo Asamoah, to be able to bring in the 28-year-old.
Pedro could also leave Chelsea with just six months remaining on his contract and having similarly fallen out of favour under Lampard.
Several MLS clubs are thought to have identified the 32-year-old forward as a possible option ahead of their summer season.
Emerson Palmieri is attracting interest from Maurizio Sarri's Juventus but that is not thought to be a likely deal to happen in the winter transfer window.