The Uruguayan youth international, who completed his move from Penarol earlier this summer, is United's only signing since David Moyes took charge at Old Trafford.
However, it remains to be seen if the 20-year-old will be a member of the first-team, or if he will be sent on loan.
Boca were reportedly keen on Varela before he joined United and they are now being linked with a possible loan deal.
And Varela is seemingly open to the prospect of a potential loan move to Argentina.
"(Going to Boca) could be a good solution. I would play with continuity for one year, always thinking of returning to United, who is the team which most believed in me," he is quoted by TuttoMercatoWeb.
"Italian clubs interested in me before arriving at United? I do not know, I would like to play in Italy, but here I'm at the top, in the best side in the world. What more could I want?"