The 22-year-old has impressed for United this season after a string of injuries at Old Trafford handed the defender his chance.
Varela was the first signing former United boss David Moyes made at the club.
The young defender could make his first cap for Uruguay in their friendlies with Brazil and Peru in March.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.