The striker made the most of his chance to start a match for the first time since October by scoring twice in the Old Lady's thumping 4-0 win over city rivals Torino in the Coppa Italia on Wednesday.
Zaza, 24, has now netted five times in just four starts and 10 total appearances in all competitions, but Allegri has told him to banish any thoughts of a loan move, despite being behind Paulo Dybala, Mario Mandzukic and Alvaro Morata in Juve's striking pecking order.
"Competition for places is good in a big team otherwise you cannot achieve good results," Allegri was quoted as saying by Gazzetta dello Sport.
"In January, even if he asks to, he will not be allowed to leave on loan. Simone must fight for his right to play here and get used to the competition.
"He must strive to play for Juventus, it should not be the other way around."
Following their victory, Juventus face an away game against either Lazio or Udinese in the quarter-finals.