The French striker has only started one league game this season and he is looking for more game time ahead of next summer's World Cup in Russia.
Arsene Wenger is eager to keep Giroud, who offers a quality option on the bench. However, the player and his agent Michael Manuello are open to leaving the Emirates if the right offer is made.
"It can make things complicated, but a clash, that kind of thing is not in Olivier's nature, nor in mine," Manuello told French football website 'Foot Mercato' about Wenger's firm stance on the striker.
"Now, depending on the offers, we will sit around a table and talk. The most important thing is to know what will be offered or not this winter, to find a better project."
"There will be approaches," Manuello added. "All clubs looking for an attacker are likely to come. We must be careful and if there is something obvious that will appear, we will try to convince Arsene to return to what has been said."
Giroud's representative dismissed talks of a return to the Ligue 1, with no offer coming from Marseille: "Olivier will not come back to France. Unless there is a change in his state of mind, to date the intention is not to return to France," he concluded. "There has been no new approach from Marseille. I have no information that Marseille was trying to contact us."