It has been suggested that the Gunners do not have that kind of money to spend this summer.
Unai Emery is said to have been handed another modest budget, with only around £45m ($57m) in the kitty at Emirates Stadium.
Campbell believes there could be ways around that, with it possible to negotiate a deal for Zaha that does not include a sizeable sum upfront.
He believes the Ivory Coast international is just what Arsenal need, telling football.london: “I would say Arsenal need to break the bank for Zaha. He's got a proven track record in the Premier League. He can hit the ground running.
“He would be an excellent addition to Unai Emery's squad and boost their attacking options. He would also create space for [Pierre-Emerick] Aubameyang and [Alexandre] Lacazette to run into in dangerous areas.
“He can carry the ball in transition and is a dangerous player. He would be my preferred option. He's strong, he's fast. He would settle in straight away.
“He can play wide left, wide right, through the centre and he's still young at 26 years of age.
“He would be my man for the club to target first and foremost as an attacking option. I think he would be a superb addition to the squad.
“Yes, he won't come cheap but the fee would be paid in instalments so it wouldn't necessarily be £60m up front.”
Arsenal are in the market for more creativity as they have seen Aaron Ramsey leave for Juventus at the end of his contract.
The ex-Gunners striker added: “[Zaha] could even solve the absence of Aaron Ramsey - who is a big loss.
“Ramsey played quite a few games as an attacking midfielder so if Emery wanted an attacking midfielder to replace his goals then Zaha could do that as well if required.
“Zaha is the player I most want to see Arsenal sign this season. It can't all be left to Aubameyang and Lacazette to do up front. Zaha would be a massive signing.”
As things stand, Arsenal appear to be prioritising deals in the defensive third of the field, with efforts being made to lure Scotland international left-back Kieran Tierney away from Celtic.