The Frenchman has struggled to play regular first team football this season, with Arsene Wenger preferring Alexis Sanchez in a central striking role, while Giroud has also struggled with injuries.
The 30-year-old has started just two games all season, both coming in the Champions League, but despite his lack of playing time, Giroud's agent says that he will not leave Arsenal in January.
"Olivier is very well at Arsenal.He will make his season here. Nothing is possible in January. He has no plans to move during the winter transfer window," the striker's agent told 'footmercato.net'.
Meanwhile the player himself last month said that he had "no doubts" over his future at the Gunners.
"I have no doubts over my Arsenal future," he said.
"As with each year, there is competition for places at the big clubs. There are a lot of attackers with different styles of play".
Despite regularly featuring on the bench, Giroud boasts an impressive goalscoring record this season, with five goals from 12 games.