The Portugal international has just seen his contract extended by 12 months thanks to an option triggered by United.
AS says Real are interested in Dalot and weighing up making a summer bid for the fullback.
Real Madrid needs to strengthen the right-side of its defence. Dani Carvajal just turned 32 and Lucas Vázquez turns 33 in June.
There is the Vinicius Tobías option from Castilla, but he is expected to be joined by a more experienced alternative, with Dalot a player now being watched.