The 24-year-old featured in Jose Mourinho's first pre-season game against Wigan Athletic last summer but joined Eintracht Frankfurt on a season-long loan a month later.
Varela was then sidelined for eight months due to injury before sitting out the German Cup final with an infected tattoo inked against the club's wishes.
According to the Manchester Evening News, Penarol have now reached an agreement with United over a transfer fee, which includes a sell-on clause, and a three-year deal could be confirmed as early as next week.
The report also claims that the Uruguayan did not report back for first-team training at Carrington on July 8, and has not featured for the club's reserves either.
Varela was David Moyes's first signing at Man United in the summer of 2013, but did not make his first-team debut until two-and-a-half years later.