The Uruguay U20 international has been linked with a £1million switch to Old Trafford, having spent time on trial with the Premier League champions at the end of last season.
Varela now looks like he'll become David Moyes's first signing since succeeding Sir Alex Ferguson as Manchester United manager, although the club is yet to confirm any deal.
The young full-back travelled to London on Thursday, but spoke to local radio station Futbol a lo Penarol in his homeland before his flight, confirming that he is on the verge of joining Manchester United.
"I will have a medical on Friday and on Saturday I join the Uruguay Under-20 national team," he said.
"I will have to learn English, Rodolfo Catino [Penarol's club treasurer] taught me something, the structure is impressive."
Penarol's treasurer, Catino, confirmed: "The deal has been agreed, we now have to discuss some points, there won't be any percentage regarding any future transfer.
"The deal can be as much as 2.8 million Euros. Guille will adapt quickly to Manchester."
Varela will find competition for a starting berth at left-back from the likes of Patrice Evra and Alex Buttner, so might have to be patient before he is handed a place in the starting XI.
But, he joins during the start of a new era for the club, with Moyes set to officially take over on July 1, meaning the South American will be given the same opportunity as everybody else, to impress and show what he can do.