The Frenchman has not started a Premier League game yet this season, but has scored four goals after coming off the bench in 13 fixtures.
The 31-year-old salvaged a point for the Gunners on Sunday as his 88th-minute goal secured a 1-1 draw with Southampton at St Mary's.
In the summer, the striker reportedly turned down a switch to Everton, but with the winter window on the horizon, West Ham United and Crystal Palace are believed to be circling.
"I'll ask myself the question again in January - that's for sure," Giroud told L'Equipe. "Loan could be best solution, but I don't know if Arsenal would want that."