The 20-year-old full-back arrived in England earlier this summer, signing a long-term contract with the reigning Premier League champions.
Varela is David Moyes's first signing since taking over at Old Trafford, but it's unlikely he'll feature in the new manager's first-team plans in 2013/14, and so a temporary loan move might be in the best interests of both player and club.
Boca are keen to secure the services of the Uruguay U20 international, and hope that the guarantee of regular football will convince Manchester United to allow the player to return to South America.
"Varela is a possibility and we like him," Requejo told Radio La Red. "The loan has been 80 per cent arranged."
The defender made just one senior appearance for Penarol before being snapped up by Manchester United, though it was his performances at the recent U20 World Cup in Turkey that convinced the club to move for his signature.