The Spanish side have lined up the 30-year-old as a possible replacement for current striker Roberto Soldado who is strongly linked with a move to Tottenham Hotspur.
According to Tuttosport, Norwich are still interested in the former Sampdoria and Udinese forward despite already reportedly having a €10 million bid rejected and are continuing to speak with the Old Lady under the radar.
Valencia’s late entry to the race for Quagliarella’s signature is thought to be a serious threat to Norwich’s chances of signing the player, as many see the Mestalla as a more glamorous destination than Carrow Road.
However, Valencia are yet to make any concrete declaration of interest to the Bianconeri as they are also looking at Real Zaragoza’s Helder Postiga and Fluminense’s Fred as alternative choices to replace Soldado should he leave.
Quagliarella has slipped down the pecking order in Turin following the arrivals of Fernando Llorente and Carlos Tevez.
As a result of this, Juve coach Antonio Conte and director general Giuseppe Marotta are working hard to find a buyer for the Italy international.
Quagliarella started 13 Serie A fixtures and came on as a substitute 14 times, scoring nine goals for the Italian champions during the 2012-13 campaign.