United had made a lucrative offer to the Ajax defender, who is also wanted by Barcelona, Paris Saint-Germain and Juventus.
Jürgen Klopp has asked Liverpool’s top brass to enter the race for De Ligt, as he wants the centre-back to be Virgil van Dijk’s long-term defensive partner.
De Ligt is expected to make a decision in the next week, but Sport claim United are already out of the running.
Barcelona are believed to be De Ligt’s No.1 choice, but the player’s agent Mino Raiola would prefer the Dutchman joined PSG or Liverpool.
PSG and Liverpool can meet Raiola’s fees, while Barcelona are offering the agent less money.