The 33-year-old was the star turn in the Sicilian club's 4-1 win on Sunday - their first in Serie A this season - with his treble including an incredible 40-yard volley.
Former Italy international Miccoli has been a bit-part figure under new coach Gian Piero Gasperini but was at his scintillating best at the Stadio Renzo Barbera.
And with his current deal set to expire at the end of the season, he hopes his performance will lead to fresh talks.
"I have not received an offer from the club," he told www.repubblica.it.
"The president said contracts are discussed in May or June. If they want to discuss it then fine, otherwise I will go elsewhere.
"But if I was asked now I would extend my stay because that is what I want."
Miccoli admitted the Chievo game had been one of his finest in a Palermo shirt.
"It is one of my best days," he said. "This is my sixth season in Palermo and every time I feel as if I have to start from scratch and prove I'm not old, or just good enough to play the last half-hour."
On the stunning goal, he added: "It was instinctive. I had not seen the goalkeeper was off his line."
Gasperini described Miccoli as his team's "special ingredient" but warned he wanted to see even more from the former Juventus and Benfica star.
"Fabrizio can still improve," he said. "He's not going to score three goals every time but he's a very important player and has an important role to play.
"He's our special ingredient."