Defender Smalling will stay at Roma until the campaign is completed, while Inter Milan will keep hold of Sanchez.
Both Serie A clubs have 10 games left to play this term and have reached agreements to extend the United players’ loan deals to ensure those fixtures are covered.
The Italian top flight is set to run until the start of August as a result of the coronavirus pandemic.
United, Inter and Roma are all still involved in the Europa League this season, and it has not yet been confirmed for which teams each player will be eligible in the competition, which is due to resume on 10 August.
Sanchez, who joined United in January 2018 and was loaned to Inter last summer, has featured 19 times for the third-placed Nerazzurri, who also recruited former Red Devils Romelu Lukaku and Ashley Young ahead of this season.
Smalling, meanwhile, has made 30 appearances for Roma this term and has scored twice.
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