The Sicilian club were interested in the Costa Rica international but the deal is now off the table.
The Costa Rica international has not been given a fair crack of the whip at the Emirates Stadium, with the likes of Alexis Sanchez, Danny Welbeck, Alex Oxlade-Chamberlain and Theo Walcott ahead of him in the pecking order.
As such, Campbell has only made four Premier League appearances for Arsene Wenger’s men since signing for the club in 2011, with loan stints at Lorient, Real Betis, Olympiakos and finally Villarreal for the 23-year-old.
With Campbell unlikely to be in first-team recognition this season at Arsenal, a move elsewhere makes sense but the 50-times capped Costa Rican will not be moving to the Stadio Renzo Barbera.
Zamparini has admitted that Palermo have opted for Serbian defender Uros Djurdjevic and as such no longer have room in their non-EU quota for Campbell.
”Right now it's impossible, I only have one non-EU slot in the squad, and I opted for the Serbian, Djurdjevic.
"Besides, I'm not in the habit of getting players from clubs like Arsenal. I'm a president who looks for less well-known players, from clubs like Cremonese or Avellino."
Campbell has shown for his country and on loan that he is a talented forward but it appears that his future is away from the Emirates Stadium.
Already something of a journeyman despite his young age, the attacker will be keen to find a club where he can prosper and play regularly this season.