Estadio Deportivo reports that United are keen to bring in the 21-year-old as a replacement for left-back Patrice Evra.
United have reportedly joined the likes of Real Madrid and Chelsea in the race to sign Spain international.
Sevilla president Jose Maria del Nido is reportedly not interested in selling Moreno unless someone meets his £25million release clause.
United have also recently been strongly linked with a move for Porto pair Eliaquim Mangala and Nicolas Otamendi.
Patrice Evra could leave United when his contract expires at the end of the season.