Given that Rodriguez is said to favour a move to a club that can offer Champions League football, it would be unusual to see such an announcement made with United still to play their Europa League final with Ajax a few days later.
Real Madrid are not prepared to discuss futures of individual players until the full season - Champions League final in Cardiff included - is over with, but the Colombian radio found out that Rodriguez has already given his nod to Jose Mourinho's side.
Per the report, the 25-year-old has been linked with a move away from the Spanish capital for some time.
However, AS report that Los Blancos may not choose to announce the deal until after their Champions League final against Juventus on June 3.
The current European champions want to recoup most of the transfer fee they paid three years ago, but a source close to the player believes they will accept an offer in the region of £50m.
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Only one thing is for certain: Rodriguez is expected to leave the Bernabeu this summer.
"His gesture at the end (of the game v Sevilla) was one of appreciation to the Madrid fans".
If true, this would be an excellent piece of business from United as Rodriguez is a supreme talent who just hasn't been given the chance to fulfill his potential at Madrid.
Rodriguez has struggled to cement a place in Zinedine Zidane's starting XI and has started only 13 La Liga matches this season.