The 34-year-old has scored 11 times in 28 appearances for the Blues during the 2020-21 campaign, including six goals in eight Champions League outings.
Giroud's contract at Stamford Bridge is due to expire at the end of June, though, and it seems likely that the France international will be leaving the capital club on a free transfer.
According to Calciomercato, Inter are chasing the striker, but the Italian champions are expected to face competition from Lazio, who might be able to offer the World Cup winner more regular action next term.
Giroud has made 15 Premier League appearances during the current season but has only featured in one of his side's last nine matches in England's top flight.
The experienced striker is also said to be a target for Turkish giants Fenerbahce. body check tags ::