The Dutchman is up for sale at Barca, which have accepted an offer from Manchester United for the midfielder.
Chelsea are also keen, but De Jong is reluctant to leave the Nou Camp.
However, Sport says Boehly has been unable to convince De Jong to join Chelsea.
Chelsea were in pole position to land De Jong who was open to a move to Stamford Bridge.
But De Jong declined Boehly's request to join the Blues via phone.