Campbell believes that Wenger needs to make substantial waves in the transfer market this summer if he wants to keep his star man, who has bagged 27 league goals this season.
"Van Persie's had an unbelievable season," Campbell told talkSPORT. "Arsenal need a few more players who want to take on the challenge, who are going to say 'I'm going to make the difference this season'.
"If they don't buy players he's going to go, I think he's going to feel there's a lack of ambition at the club. Arsenal need a few players who can make the difference, on the field and on the bench."
Van Persie, whose current deal runs out at the end of the season, signed for Arsenal from Eredivisie side Feyenoord in 2003.