The Frenchman, 33, is looking for a January exit after falling out of favour under Frank Lampard.
Sky Italia says Giroud's agent Michael Manuello was in Milan for talks yesterday.
Transfer guru Fabrizio Romano's report adds that Tottenham midfielder Christian Eriksen's representatives are also due in Italy to discuss a move to Inter.
Exclusive: Olivier Giroud agent met Inter directors today in Milano. The French striker would be ready to join and agreed personal terms (contract until 2022) - but talks are still on between Inter and Chelsea, no agreement yet btw the two clubs. @SkySport#Inter#Chelsea#CFCpic.twitter.com/zcumNneQjU— Fabrizio Romano (@FabrizioRomano) January 9, 2020