Requejo is club secretary at the Argentine outfit, who have been open in their desire to bring a full-back on board this summer.
They consider Varela to be a top target, with the 20-year-old unlikely to figure prominently in David Moyes' plans for the foreseeable future.
The Uruguayan remains Moyes' only capture since taking the managerial reins at Old Trafford, but the Red Devils have acquired his services as part of a long-term plan.
Varela has signed a five-year contract with the reigning Premier League champions and appreciates that he will have to be patient in his pursuit of regular first-team football.
Taking that into account, he may be willing to return to South America on a season-long agreement.
Boca are optimistic regarding their chances of putting a deal in place, with Requejo claiming that positive discussions have been held.
He told Radio La Red: "Varela is a possibility and we like him.
"The loan has been 80 per cent arranged."
Varela has played just 23 minutes of senior football at Penarol, but was among those to catch the eye at the recent U20 World Cup in Turkey - highlighting why United were so keen to get him snapped up.