The Italian sides will reportedly make their move at the end of the season, and as he will be approaching 32 by then, Giroud will surely be more tempted to leave than he was by Everton.
Premier League clubs like West Ham United and Everton were the frontrunners for his signature but Giroud instead elected to stay in North London.
France manager Didier Dechamps clearly has much faith in Giroud, with even teenage prodigy Kylian Mbappe forced out of the starting XI to make way for the Arsenal striker.
It's a transfer which does have some merit.
Giroud has scored one goal in a 4-3 victory over Leicester City on the opening day of the season but has been limited to seven consecutive substitute appearances in the Premier League this term.
During the summer, Giroud reaffirmed his commitment to the Gunners by remaining at the Emirates Stadium, despite interest in his signature from both English clubs and overseas.