The France international has been linked with an Emirates exit as he seeks regular playing time in order to boost his World Cup hopes.
He has only started one Premier League game this season, with boss Arsene Wenger preferring summer signing Alexandre Lacazette.
Despite his limited appearances, the 31-year-old has bagged seven goals for the Gunners.
He was linked with a move to Everton in the summer and they were likely to go back in for him when the transfer window opens next month, along with Premier League rivals West Ham.
But any chance of a move is unlikely with his latest injury setback.
Giroud was forced off with a hamstring problem in the 78th minute of Tuesday’s Carabao Cup win over West Ham.
And according to L’Equipe, he’s been ruled out of action for six weeks.
Wenger will now be without the striker for the busy festive run of fixtures, where squad rotation could have seen Giroud feature more regularly.
Arsenal face six games in just over two weeks, starting this Thursday as they travel to in-form Crystal Palace (8pm).