The North London outfit are currently at the top of the table after five games of the campaign, but Graham believes that a few more additions will keep them in contention.
"They definitely need a couple more [players]," Graham told talkSPORT. "The squad is a little weak and they need a 25 league goal centre-forward. That would be a great signing in the [January] window.
"I think Arsenal will be there or thereabouts at the end of the season, I really do. If they can get one or two more [signings] in the winter, I think they've got a great chance."
The Gunners failed to sign a striker in the summer window, but broke their club record by spending £42.5m on Mesut Ozil from Real Madrid.