The Colombia international has been tipped to leave the Bernabeu, with Jose Mourinho a huge admirer of the Real man.
Reports suggested Real had offered the playmaker to United in a bumper summer move.
However, according to Spanish transfer outlet Don Balon, Rodriguez has other ideas.
They say the former Monaco man wants to stay at Real and he's happy in the Spanish capital.
Rodriguez, 25, struggled to get game time under Zinedine Zidane last season.
He started just 13 La Liga games, netting eight goals.
Starsport understands United are closing in on Romelu Lukaku after agreeing a £75m fee with Everton.
Personal terms have been agreed and a deal is expected to be announced within 24 hours.
With Lukaku set to join United, Jose Mourinho has ended his interest in Real star Alvaro Morata.
