Giroud has been a bit-part player at Chelsea this season and has not played a minute of Premier League football since the end of August.
He also remained an unused substitute in Chelsea’s win over Lille in the Champions League on Wednesday night and is down the pecking order under Frank Lampard.
There are suggestions if his situation does not improve, the striker is likely to consider the option of escaping Chelsea in the January transfer window.
And according to Italian outlet Calciomercato.it , he could have suitors in Italy in the form of Serie A giants AC Milan once the window opens in January.
The Rossoneri are in the market for a striker and are keeping tabs on a number of players ahead of the winter window.
The club are yet to take any concrete measures, but Giroud has been suggested as a player they could look to sign in January.
And if he continues to warm the bench at Chelsea, the striker could welcome the chance to move elsewhere in the new year.