The 30-year-old was heavily linked with a summer move to Upton Park, after Juventus completed the signings of Carlos Tevez and Fernando Llorente.
The Hammers have struggled for goals this season, with record signing Andy Carroll yet to feature due to injury.
Manager Sam Allardyce is set to sign a new striker in January, and had his sights set on the experienced Italian forward, who has also been attracting interest from Lazio.
But he may well be forced to abandon his interest according to the player’s agent Giuseppe Bozo, who insists his client has no desire to quit the club, despite the fact he has started just two league games this season.
“I am not aware that there have been any contacts between Lazio and my client, because Fabio has no intention of leaving Juventus in January,” he is quoted as saying on Calciomercatonews.
“[Juventus manager Antonio] Conte does not want to deprive himself [of Quagliarella]. We cannot say that Fabio is treated as the fourth striker after Carlos Tevez, Fernando Llorente and Mirko Vucinic.
“Plus the fact he is playing in a team that is fighting for the title is an extra motivation for him and he will not give up.”