The Biancocelesti will have an option to buy Pereira, 24, for a fee of €27m next summer.
Pereira fell down the pecking order at Old Trafford following the Premier League restart last season.
Before then, he had been featuring regularly for Ole Gunnar Solskjaer’s side.
But with the arrival of Donny van de Beek from Ajax, the Belgium-born Brazil international has few prospects for game time.
Lazio, who offer Pereira both Serie A and Champions League football, could make his debut against Inter at the weekend.
It would see Pereira face his former Man United teammates Romelu Lukaku, Alexis Sanchez and Ashley Young.