It is understood that would be an unlikely set of circumstances with Arsene Wenger having consistently backed the French global, who has often borne the brunt of criticism when Arsenal's form has hit the rocks.
Giroud has found a consistent starting spot in Arsenal's attacking line hard to come by this season, with Arsène Wenger rotating the Frenchman with Danny Welbeck and Alexis throughout the campaign.
Speaking at a press conference last week Giroud said: "I want to win the Premier League with the club. Olivier knows what he is capable of, and he knows I have confidence in him".
Trump partially denies Comey's testimony, mum on existence of recordings
He also said that would be "100%" willing to be questioned under oath. "No collusion, no obstruction", Trump said. When pressed on the matter, Trump said: "Well, I'll tell you about that maybe sometime in the very near future".
Giroud recently indicated that he will leave Arsenal should he not be assured of first team action by saying, "It is true that I have had limited playing time but it was for a certain amount of time, it is true there were things against me".
And with Giroud's game time likely to decrease next season, the 30-year-old is open to leaving.
"It [a transfer] will be a well-thought out decision".
West Ham are believed to be monitoring the French striker and are willing to pay Arsenal £20m to secure his services for next season.
They have also been hoping to sign Chelsea's Michy Batshuayi on loan, although that deal is up in the air because the club now look certain to dump Diego Costa.