The 33-year-old has been left sitting on the bench to wait for his chance this season after Tammy Abraham was given the nod to lead the line for the Blues this term.
A nod which has proved beneficial for Frank Lampard as Abraham has scored eight goals already in the Premier League this season.
Meanwhile Giroud has only started once this season under Lampard, and his future has now come into doubt.
He revealed on Monday that if the Blues force him to leave, he won't be afraid to depart Stamford Bridge.
"I feel in good shape physically and I lead a healthy lifestyle. I want to enjoy myself and play matches. That could be for Chelsea – who are my first choice – or elsewhere. But if they force me to make a decision I will do it – just like when I left Arsenal."
According to Nicolò Shira, the 33-year-old has received two offers to play in the MLS.
New York City and Vancouver Whitechaps are the two sides reportedly interested in the French forward.
Olivier Giroud was brought to Chelsea from Arsenal in January 2018 by then manager Antonio Conte, and the former Blues boss is also interested in a reunion with the French forward at Inter Milan in the Serie A.
French National Team coach Didier Deschamps has also advised the forward to assess his options after a lack of game time under Frank Lampard this season.
"You know, Olivier suffers his situation. Before January, nothing will move. After, it will be up to him to see. I hope he will have more playing time," Deschamps said.
With Chelsea currently under a transfer embargo until next summer, Frank Lampard will be unlikely allow the 33-year-old to leave the club in January, but a summer move is nearing likely to be on the cards.