The Red Devils are believed to have reached a full agreement with Barcelona for Frenkie de Jong, with the Netherlands international being identified as the club's leading transfer target this summer.
However, Man United face a battle to sign the 25-year-old, who has travelled with his current side to America for their pre-season tour.
Speaking ahead of Tuesday's friendly with Crystal Palace, Ten Hag revealed that his side are bidding to sign a holding midfielder but insisted that "it has to be the right one".
"We are looking for a player who can play in the holding midfield position but it has to be the right one," Ten Hag told reporters.
"There are not many in that position capable of the level we demand. When we can't find him, we have to deal with the players in our squad now and we will develop one in that position.
"I will not react on a certain player. We need the right player. We have a list and we qualify as the player who has the competence to play that role. We will strike the moment the player is available."
Man United were strongly linked with Kalvin Phillips before he joined Manchester City from Leeds United, while Declan Rice is also believed to be admired by the club, but he has been priced out of a move, with West Ham United thought to value the midfielder in excess of £100m.
Ten Hag has claimed that he "would like to sign English players", but it has not been possible this summer due to their asking prices.
"I would like to sign English players, because I think there is only one criteria and that's quality in combination with the price. It looks like English players are quite expensive. It's a fact you cannot deny. In the end, it's about quality," he added.
Man United have reportedly agreed to pay €75m (£63.5m) plus add-ons to sign the former Ajax youngster but are still struggling to convince him to leave Barcelona.
"I prefer to stay with Barcelona. Barcelona is just my dream club. Also from a young age. I just said it too. I've never regretted my choice despite the fact that I had hoped for more in terms of prizes than I've achieved so far. But I have never regretted my choice," the midfielder told ESPN earlier this summer.
De Jong, who still has another four years left to run on his contract at Barcelona, was a key player for Xavi's side last season, making 46 appearances in all competitions, contributing four goals and five assists in the process.
The Dutchman has represented the Catalan giants on 138 occasions since arriving from Ajax in the summer of 2016, contributing 13 goals and 17 assists in the process, but the La Liga team are keen to sell him in the current market in order to balance the books.
Man United have already signed three new players during this summer's transfer window, bringing in Tyrell Malacia, Christian Eriksen and Lisandro Martinez.