United hope to do business for around £50m.
However the midfielder may need more persuading to leave than Barca do to let him go.
The financially-crippled Spanish club need to cut costs and boss Xavi us understood to be prepared to let the Dutch midfielder leave.
Yet De Jong, 25, said this week he still believes he is at his “dream" club and wants to stay.
Ten Hag is hopeful he can convince him to change his mind.
Barca will demand the £67m they paid Ajax in 2019, though United believe they can cut that asking price significantly.