The 20-year-old Uruguayan is the only man through the door at Old Trafford this summer, but it is unlikely he will feature in David Moyes's first-team plans.
Boca were believed to be interested in signing Varela before his switch to Old Trafford and are thought to be keen on a short-term loan deal.
"[Going to Boca] could be a good solution," Tuttomercatoweb quotes him as saying.
"I would play with continuity for one year, always thinking of returning to United, who is the team which most believed in me."
Varela signed from Uruguayan side Penarol.