The 22-year-old is thought to have been of interest to United for some time as Jose Mourinho looks for a long-term solution for the troublesome left-back position.
Last month it was claimed that Mourinho was weighing up making a bid for the Spaniard, having watched him in action against United in the Champions League, and now Benfica CEO Domingos Oliveria has hinted that a deal is possible.
"All of the Benfica players have a certain market," he is quoted as saying by IB Times. "Now you have some differences, the oldest guy we have in the team is Julio Cesar who is 38 years old and youngest is Mile Svilar who is 18.
"The players with over 30 years, it is difficult to transfer them although for example Jonas, our best striker, when we hired him he was already 30. But for a player who is 25, 26, 27, or younger at 22, 23, 24, there is a huge market. I am not talking specifically about Grimaldo, but all players with those conditions, they have a market.
"We do not want to close the door to anyone. We don't want to force them to stay here. We want them to stay as long as they can. And while they are here they are happy, but once both parties agree on a transfer, usually the player leaves but as mentioned before, leave with a good relationship with the club."
Grimaldo, who moved to Portugal from Barcelona two years ago, is thought to be available for around £8m.