Campbell, however, warned that success on the pitch, and a healthy balance sheet, may be incompatible in the short term.
He told the Mirror: "Arsenal have established this model of financial prudence, they have a fantastic new stadium, they are bringing the club's debt down ahead of schedule and everything is tickety-boo off the pitch.
"They are making money, they are in good shape and everything is well-run... but they are not winning. The real sting is in the punchline.
"Changing the manager isn't going to make any difference. If there are any Arsenal fans who are tempted to call for Arsene Wenger to step down, is a new manager going to get any more firepower in the transfer market?
"Unless someone produces £100m and Wenger brings some big signings to the club, I can't see van Persie changing his mind.