Rodriguez was one of the stars of the 2015 World Cup in Brazil with his excellent performances for Colombia that earned him a move to Madrid.
But he has struggled to find a regular starting berth with Real and is allegedly looking for other opportunities.
Any potential suitors would need to match his release clause though, which stands at £67-million (R1.2-billion), which cuts down the number of clubs significantly.
Manchester United and Chelsea have been mentioned as clubs in the frame, along with West Ham United, though that may be wishful thinking on the part of Hammers fans.
Rodriguez started 17 La Liga matches last season and did not make it off the bench in the UEFA Champions League final.