A return to the Premier League is considered to be the most likely outcome, with a loan spell at former club Tottenham having already been speculated on.
This comes off the back of a Wayne Rooney interview with the BBC when he advised the club to focus on lower profile players and build a new team around them rather than looking for short-term solutions.
"He's a fantastic player but Cristiano is unique".
"I know last season was not the best season at Real Madrid, but hopefully next year will be better".
Though Zidane returned as coach in March, replacing Santiago Solari, Madrid is desperate to restore itself as a champion in soccer's greatest tournaments.
Eden Hazard, who will be officially unveiled as Real Madrid player on Thursday, was one of the priority signings for the manager Zinedine Zidane.
"His behaviour has been impeccable, he is the most skilful player I think has ever played for Chelsea Football Club".
Guardiola has now described the signing of Eden Hazard at Real Madrid as an awesome one claiming that the Belgian is one of the best players he has ever seen.
Alexis Sanchez's arrival at Old Trafford in January 2018 is arguably an example of quickly things can go wrong for an older star signing, although he could also be on his way out ahead of next season.
Rodriguez, also linked with United as well as Liverpool FC and Arsenal, could generate approximately $33 million.