The 25-year-old defender featured just 11 times under Louis van Gaal last season and is one of the players who United are willing to offload this summer.
Reports in Portugal suggest that Benfica will only sell Gaitan if his €35 million (£25.1m) release clause is triggered but Rafael’s representative claims United are willing to use the Brazilian as part of a potential deal.
"Benfica and Manchester United are in negotiations over Gaitan and one offer includes Rafael to join Benfica,” Cassiano Pereira told Record.
"Rafael wants to join Benfica. It's a big European club. If the talks proceed, it will not be difficult to reach an agreement."