According to reports in Italy carried by A Bola, Carlo Ancelotti's side are ready to include left-back Coentrao in any deal for the France international.
Almost every summer Real Madrid identify one top target who they pursue aggressively over the course of the off-season. Last year that was Gareth Bale, this term it could be Pogba.
The France international is set for a big summer with France at the World Cup, and while Juventus remain desperate to keep him in Turin, recent noises from his camp suggest a move could be on the cards before the tournament.
The report claims Madrid are willing to include one of Alvaro Morata or Angel Di Maria if Juventus are not interested in Coentrao, while PSG are preparing a cash-only €70m offer of their own to rival the Spanish giants.
Pogba, who fell out with Sir Alex Ferguson at Old Trafford, has been mentioned as a possible summer target for Moyes.
Likewise, Coentrao was hotly tipped to join United both last summer and in the January transfer window and reportedly remains a target heading into the World Cup.
The 26-year-old Portugal international stayed in the Spanish capital despite interest in January, although it doesn't look like he features in Ancelotti's plans.
He has made just six La Liga appearances so far this season.