The Italian website reports the 31 year old may consider a summer switch away from the Emirates if his game time does not improve between now and the end of the season.
Juventus, Inter Milan and AC Milan are all believed to be keen on the French international. Juve are seeking a possible replacement for Mario Mandzukic with Giroud being seen as someone with a similar profile. Inter meanwhile are looking for suitable backup for number nine Mauro Icardi.
AC Milan are the least likely out of the trio to make a move for the player as they did sign two forwards in Andre Silva and Nikola Kalinic in the summer, but they may still look to strengthen their striking options again at the end of the season.
The Frenchman has confirmed in recent days he was close to moving to Everton before the start of the campaign, but he opted to stay with the Gunners despite knowing he would be behind new signing Alexandre Lacazette in the pecking order.