Giroud is out of favour at Stamford Bridge under Frank Lampard and open to a move away this month.
CEO Beppe Marotta said: “I won't deny we spoke to Olivier Giroud's entourage, we will evaluate the situation.
“What doesn't happen on the transfer market today could happen tomorrow. Victor Moses is a candidate."
Inter face competition for his signature in the form of Aston Villa, who are keen to loan Giroud until the end of the season, after losing Wesley to injury.