With Arturo Vidal (thigh), Andrea Pirlo (hip), Andrea Barzagli (Achilles) and Giorgio Chiellini (calf) all unavailable, it now looks as though Carlos Tevez could also be set for a spell on the sidelines.
Reports in the Italian press claimed that the Argentina forward limped out of training on Wednesday with a suspected hamstring injury.
That would represent a major blow for the champions, with Tevez having scored 19 goals last season as Juve saw off the threat of Roma to take a third consecutive Scudetto.
It would also leave Sebastian Giovinco and Fernando Llorente as Allegri's primary striking options for his first home match in charge.
Juve coach Allegri could, however, be boosted by the return of close-season signing Alvaro Morata, who has made a swift recovery from the knee surgery he had in July.
Morata joined from Real Madrid with the promise of increasing Juve's attacking threat and, though a start against Udinese is unlikely, he could play a role from the bench.
Chiellini's absence has been the subject of some controversy, with the defender having been withdrawn from international duty by his club.
Juve were forced to defend the decision to recall Chiellini amid criticism from the Italy hierarchy, who argued that he should have stayed with his country until the end of the international break.
While Allegri's tenure started with a 1-0 win over Chievo, Udinese were also victorious in Andrea Stramaccioni's first game at the helm - beating newly promoted Empoli 2-0.
Stalwart striker Antonio Di Natale scored twice in that match to defeat the club where his career began almost two decades ago.
That double added to the 36-year-old's incredible five-goal haul against Ternana in the Coppa Italia, and Udinese will need their talisman to be on top form if they are to upset the odds this weekend.
Udinese, who finished 13th last season, have not beaten Juve in the last six attempts and lost twice to them in the 2013-14 campaign.