The Gunners have been left short at the back following injuries to Mathieu Debuchy and Laurent Koscielny.
Manager Arsene Wenger admits that he is planning to bolster his rearguard in January.
And Parlour feels that the Dutch centre-half would be a good addition to the Arsenal defence.
“Van Dijk would be a good signing,” Parlour told talkSPORT. “Arsenal look really short at the back. Koscielny is out now for a little while, which is another blow.
“Arsene is just hoping he can get through to January. He’s got to go out and buy a couple of defenders.
“He needs to strengthen if they’re going to have a serious run on the Premier League title. You need to have a big squad.”
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