Quagliarella's ability to find the net has been attracting the interest of clubs in the Serie A, such as Juventus and Napoli.
"I will tell the newspapers that I am and have always claimed to be very happy with Udinese. I'm proud to wear this jersey and I hope to score more goals here," the Italian international said in an interview.
Quagliarella scored in Udinese's win over Zenit St Petersburg in their UEFA Cup clash at home and will be counted upon to deliver the Zebrette into the next round.
"We hope to move forward, it is our dream," revealed Quagliarella. "What matters is we go to Russia and not make this mistake of trying to maintain the lead at 2-0. We must try to find a way to score."
The 26-year-old has scored 16 goals in all competitions this season under coach Pasquale Marino.