Van Persie is entering the final year of his current deal.
"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."