The Gunners currently sit five points clear at the top of the table following a 2-0 win at the Emirates Stadium over rivals Liverpool on Saturday.
However, Robson feels that Arsenal will eventually stutter unless they can find help for Olivier Giroud to ease the burden in attack.
"I don't think they need that many new players in January, though they probably need a second centre-forward just in case Giroud picks up an injury," Robson told talkSPORT.
"Bendtner has not been good enough, we know that, so we probably need another main striker. We can't get more creative midfield players, we're inundated with them.
"If Arsene Wenger keeps his cool and he doesn't get riled, if they lose a couple of games, I think they have every chance of staying right at the top."