The former Chelsea forward insists he has never wanted to play for any other side, though he acknowledges he needs more game time at the Allianz Arena
The 34-year-old has made just 12 appearances in the Bundesliga in 2012-13, with a further six coming in the side's DFB-Pokal and Champions League campaigns.
But despite sitting behind Mario Mandzukic and Mario Gomez in the pecking order, Pizarro has revealed he has never wanted to play anywhere but the Allianz Arena, even during his brief spells with Chelsea and Werder Bremen in recent seasons.
"I would love to stay," he told AZ. "I wanted to stay here forever, even when I went to Chelsea."
Despite his insistence that he wants to remain with Jupp Heynckes' side, Pizarro has acknowledged he needs more playing time in order to sustain his sharpness.
"I need more games," he declared. "I have had no practice."
Pizarro is one of the names linked with a move away from the Bundesliga leaders this summer, when Pep Guardiola assumes control of the first team.
The likes of Robert Lewandowski, Luis Suarez and Neymar have been linked with a switch to die Roten ahead of next season, meaning the Lima-born forward could still be forced to look elsewhere for first-team football.