The Gunners have lost their first three Premier League matches of the season and sit bottom of the table heading into the international break.
Campbell does not think that any top manager would want to take on Arteta's job.
He said on Sky Sports News: "If Mikel Arteta gets the sack, which big-name manager is going to put his reputation on the line and have no significant funds to go and change what he's seeing?"
Asked if Arsenal should pursue Conte, Campbell added: "If you back him.
"Arsenal with all their players fit will be okay.
"But if I'm Antonio Conte and I'm looking at that yesterday, I wouldn't go anywhere near it."
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