That's according to Spanish newspaper Marca, who claim Real Madrid and Monaco have already opened talks over a transfer, although the two clubs are so way apart over the valuation.
United were mentioned as suitors for the Colombian international earlier this month, following Colombia's elimination from the World Cup at the hands of hosts Brazil.
The Old Trafford club were thought to be considering a bid for the playmaker, with Real Madrid's Angel Di Maria another potential contender.
Real Madrid interest
But Marca reports bad news on two fronts for United's transfer hopes. It looks like Real Madrid could be preparing to sell Di Maria to Paris Saint Germain for around €60m, and using the proceeds to sign Rodriguez from Monaco.
Rodriguez was signed by the Ligue 1 side for close to €40m from Portuguese side Porto last summer.
Clubs some way apart
But with Monaco looking for €115m and Real Madrid only willing to go as high as €85m so far, a deal looks some way off yet. Talks have only opened recently, and there's plenty of time for negotiations, but it's unlikely Real Madrid will be keen to shell out a world record fee for the playmaker.
He was excellent for Colombia at the World Cup, but he's not at the level that Gareth Bale and Cristiano Ronaldo were when Real Madrid splashed out on transfer fees around the €100m mark.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: https://www.givemesport.com/writeforgms