"Arsenal have great players," he said. "But with everybody fit, I still don't think it's enough. They've got to get a few players who can make the difference."
Campbell would know about making a difference and winning trophies at Arsenal, the powerful central defender made more than 200 appearances for the club, winning three FA Cups and two Premier League titles along the way.
One of those championships came as part of the "Invincibles" who went through the 2003-04 season unbeaten.
Not only does Campbell think the current squad is not good enough, he also cast doubt on whether the club is determined to make the changes necessary to chase trophies in multiple competitions.
"You've got to ask yourself," he said, "where are Arsenal going? Do they want to actually win anything?"
Wenger has been routinely criticized for stinginess in the transfer market in recent years. The 62-year-old Frenchman has shown a general reluctance to buy the type of proven (and expensive) superstars that many Arsenal supporters believe would result in championships.
"You've got to push the boat out," Campbell told the BBC. "Swallow your pride and pay a little bit more, put a bit more on the table and get the players in."
Last summer, the departures of Cesc Fabregas and Samir Nasri brought a fresh round of criticism as Wenger refused to spend big to replace his exiting stars.
Although the team's improved form over the course of the season has quieted the ridiculous early season calls for Wenger's sacking, he faces another trying summer as Robin van Persie has so far refused to sign a contract extension with the Gunners.
It has been widely speculated that the striker is waiting to see whether his manager will bring in top-level players over the summer before deciding on his future.
Wenger is always keen to develop young players through the club rather than buying older established stars, but Campbell suggests that the time has come to do a rethink.
"You need the players who are going to come in for two or three years and make the difference. It's all about the here and now," he said.
With another profitable, but trophy-less, season coming to a close, Campbell echoes the sentiments of a growing number of Arsenal supporters.
Whether Wenger is listening or not remains to be seen.