Defender Smalling moved on loan last August and has made 30 appearances in all competitions, impressing to such an extent that coach Paulo Fonseca has said he would like to keep hold of the centre-back for longer.
"I will do everything I can to keep him at Roma next year too. I know he wants to stay, let's see what happens," Fonseca said.
Sanchez, meanwhile, has featured 19 times for Antonio Conte's side during a campaign that has been disrupted by injuries.
The forward, who previously played in Serie A with Udinese, has scored just once so far for the Nerazzurri, his solitary strike coming in a 3-1 league win away at Sampdoria.
With the coronavirus pandemic forcing a lengthy suspension to the schedule, United have agreed both players can stay at their current clubs to see out the Italian campaign, which runs until early August.
The Red Devils had already announced goalkeeper Dean Henderson will continue at Sheffield United until the Premier League season is completed.