Ten Hag has admitted that the club would ideally have made more signings at this stage but stressed the importance of not bringing in players for the sake of it.
"That would be a good situation (to have signed more players ahead of the season). But I have a squad and I'm happy with the squad," the Dutchman said during Friday's pre-match press conference ahead of the team's Premier League opener with Brighton & Hove Albion on Sunday.
"The current squad, they make good progress. I'm happy with the signings until now. We just don't need any player, you need the right players and that's the point where we're working all together.
"If it's not the right player, no (would you be happy signing anyone). Then I'm happy with the current squad. We need the right players.
"It's about the right players and there are many but I cannot give comments about a player who is under contract in another club. When we have news, we will bring it.
"You work with the current squad and then you develop players who are in your current squad. In this moment, there are players in that position and they perform really well."
Man United have been locked in discussions with Barcelona over De Jong for the last eight weeks, but it is understood that a deal is still not close to going through.
Man United have allowed a number of players to leave the club this summer, with Paul Pogba, Jesse Lingard, Nemanja Matic, Edinson Cavani and Juan Mata leaving on free transfers, while Lee Grant retired.
As well as a centre-forward and a central midfielder, Man United are also likely to bring in a goalkeeper before the end of the window following Henderson's loan move to Nottingham Forest.