France international recently joined Chelsea from Arsenal in January.
According to French media outlet Le Foot, Chelsea could send the 32yr old on loan with the option of securing a permanent deal when his Blues contract expires.
Giroud prior to his arrival at Chelsea was heavily linked with Marseille.
Sarri has been forced to ch0ose between Olivier Giroud and Alvaro Morata in the current league season.
With the Blues starting the campaign unbeaten in all competitions and with star man Eden Hazard chipping in with his fair share of goals, all is rosy at the club.
But Giroud who won the 2018 World cup with the Les Bleus side in the summer, is believed to looking for a regular football.
Morata has scored 15 goals and contributed six assists in 48 outings since moving from Real Madrid compared to the 12 goals and three assists from Giroud.
Under Chelsea boss Antonio Conte, Giroud was preferred over the Spaniard.
After a slow start to the Premier League, Maurizio Sarri seems to have preferred Morata over Giroud after netting five goals in the current football season.
Giroud recently ended his goal draught with Chelsea with a goal against Bate Borisov in the Europa league.
That had followed a run of 1,000 minutes without a goal for either club or country before Giroud struck in the UEFA Nations League win over Netherlands in September.
Chelsea sit in third place at the moment despite being on international break.
Their 12 match unbeaten run in the league, along with Liverpool’s and Manchester City’s, means it is the first time in history that three teams in England’s top division have done so.