The Uruguay forward joined the Italian giants from Atletico Madrid shortly after Inter sold Samuel Eto'o to Russian side Anzhi Makhachkala.
Juventus entertain Parma in Turin on Sunday hoping to prove their worth to new coach Antonio Conte.
The Bianconeri, who will not play in Europe this season, are boosted by the arrival of forward Mirko Vucinic from Roma.
Two teams that could present Milan and Inter with fierce competition are Napoli and Roma.
The clubs have bolstered their squads in the transfer market.
Former Udinese star Gokhan Inler is one of Napoli's 13 signings.
Fiorentina entertain Bologna in Florence, in the same stadium where Italy beat Slovenia 1-0 on Tuesday night to secure a place in Euro 2012.
Udinese begin life without Alexis Sanchez when they travel to Lecce on Sunday.
The Chilean winger scored 12 times in 31 games to help Udinese finish fourth last term but moved to Barcelona this summer in a £23m transfer deal.
Siena, who were one of the three teams that gained promotion to the top flight, make the journey to Sicily to face Catania.
Novara will play their first Serie A game in 55 years when they square off against Chievo in Verona.
Atalanta, another club that returns to the top flight having finished first in Serie B, take on Genoa at the Luigi Ferraris stadium.