Rodriguez has endured a difficult season at Real Madrid.
The Colombia international has been restricted to just 29 appearances across all competitions.
His lack of game time means he is expected to depart the La Liga leaders at the end of the season.
And Spanish outlet Don Balon claim he is close to joining Manchester United .
Rodriguez has supposedly consented to join the Red Devils after agreeing terms via his agent, Jorge Mendes.
Mendes also represents United boss Jose Mourinho and his influence is proving key to the deal.
David de Gea is set to leave Manchester United for Real Madrid
Rodriguez could move to Old Trafford as part of a deal that sees De Gea finally join Real.
The Spain international came close to joining the Champions League holders in 2015 only for a faulty fax machine to scupper the deal.
Real are confident they can sign him for £30million if Rodriguez is included as part of a deal.