Manchester United have been linked with a move for the Real Madrid star all summer.
The Red Devils are aiming to rebuild after a goal-shy season under Jose Mourinho last term.
Rodriguez looks increasingly likely to leave Real after making just 32 appearances under Zinedine Zidane as the club won La Liga and the Champions League.
The Colombia international joined the Spanish giants from Monaco in 2014 after his exploits at the World Cup in Brazil, where he finished as the tournament's top scorer.
But, though he was an ever-present under Carlo Ancelotti, his Real Madrid move has backfired and a parting of ways now consequently looks inevitable.
Reports in Spain last month suggested Mourinho wants Rodriguez, and his team-mate Alvaro Morata, to bring some much-needed excitement back to Old Trafford.
United managed to find the net just 54 times from 38 Premier League games - with a staggering 19 of those belonging to Zlatan Ibrahimovic.
And they are still striding for the gung-ho football that made them so entertaining under Sir Alex Ferguson, with David Moyes, Louis van Gaal and Mourinho all failing to bring it back.
But Don Balon say United's failure to meet Real's asking price for Rodriguez is holding up a potential transfer.
It is said the Red Devils are willing to pay just £35million for him, while Madrid want something in the region of £55m.
As a result, the player's agent Jorge Mendes will now supposedly hold talks with United in order to convince them to cough up.
Real are in a hurry as they want to seal a deal for Real Betis' Dani Ceballos but, if they fail to get rid of Rodriguez, he could end up at Barcelona instead.
Source: Daily Express