Giroud has been limited to a bit-part role for the majority of the current campaign, making just 11 Premier League starts due largely to the form of Alexis Sanchez in a central attacking position.
Sanchez's own future remains shrouded in uncertainty as he approaches the final year of his contract at the Emirates Stadium, which could see Wenger enter the transfer market in search of a replacement.
Alexandre Lacazette is one of the names being linked with the Gunners, but The Mirror reports that Giroud would mull over his options if he was not guaranteed more regular first-team football next season.
The 30-year-old is understood to be wanted by Ligue 1 side Marseille and could be tempted into a move if it would improve his chances of being named in France's World Cup squad next year.
Giroud has scored 98 goals in 225 appearances for Arsenal since joining the club five years ago.