The France international, 30, has started just six Premier League games this season for the Gunners, and continues to be in and out of the starting line-up as Arsene Wenger prefers Alexis Sanchez in the centre-forward role.
Despite his lack of involvement this season, Giroud has snatched some important goals for Arsenal and has netted five goals in five games since the start of 2017.
Goal France (via Metro) now claim Marseille have identified Giroud as an ideal attacking target this summer as they look to bolster their options upfront.
Giroud was reportedly unhappy at his bench role for Arsenal this season but only last month signed a new deal to remain at the club until summer 2019. However, should he continue to be in and out of the side until the remainder of the season, the Frenchman could look at his options available to him this summer.