So far, Ten Hag has added Tyrell Malacia, Christian Eriksen and Lisandro Martinez to the United squad that finished sixth last season.
However, the former Ajax boss is not done in the summer transfer market.
Ten Hag told The Athletic: “We are looking for a player who can play in the holding midfield position, but it has to be the right one.
“There are not many in that position capable of the level we demand.”
United have been strongly linked with Barcelona midfielder, Frenkie De Jongn.
It is believed both clubs have agreed a £67m fee with the LaLiga side, but De Jong is not very eager to move.