The Daily Mail's David Kent reported that the clubs are currently €10 million apart in negotiations, with Los Merengues having offered €75 million, while Monaco are holding firm on the Colombian's €85 million tag.
Later on Sunday, The Independent's Tom Sheen reported that Real Madrid could buy Rodriguez, who was allegedly seen boarding a flight to Madrid, for €90 million in the next 48 hours.
It's easy to say from an outsider's perspective, what with the hidden fees, salary, add-ons and other clauses that make such massive deals a complex matter, but even if Real pay the largest rumored amount, they'll find value in excess.
A triumphant 2014 World Cup, in which Rodriguez won the Golden Boot, has undoubtedly put the attacker in a brighter light, but this recent rise has been coming for some time. WhoScored.com breaks down his tournament in Brazil:
Upon moving to the French Riviera from Porto, alongside Joao Moutinho, Rodriguez was regarded in the right circles as a talent who would one day go on to achieve wonders.
I believe that’s true. Why? Because a player like that is difficult to keep at a club when you have Real Madrid and Barcelona looking around, and without a doubt there will be people who will be watching them play and thinking about buying him.
Is this the year that he will move? Certainly not because he is with Monaco and they will play Champions League next season and they are a big club in France. But certainly in the next season or two he will want to move somewhere else.
Still just 23 years of age, it's remarkable that he's excelled so swiftly in the past year and with such a weight upon his shoulders, but Squawka illustrates just how essential he was to the Monaco cause last term:
Needless to say the Ligue 1 giants may not have sealed their second-place finish without his presence in attacking midfield. He showed tenacity spliced with a more elegant brilliance that would go down so well at the Bernabeu.
Graham Ruthven of beIN Sports pointed out just what a threatening assortment Real would have with Rodriguez among their ranks, while the Daily Mail reported that the move may hinge on Angel Di Maria's future:
At 23, the malleable finisher has another decade at the elite level ahead of him. It's around the age Real wished they could have acquired Cristiano Ronaldo at.
Gareth Bale, another player whose purchase was made on the back of resplendent, although potentially temporary, form, is already proving that he'll likely go on to repay his similar price tag and then some, to which Rodriguez can do the same. They could make a dominant tandem for years.
In Bale's first season at the club, Los Blancos took the Champions League crown but just missed out on a La Liga title. By amassing an even greater stockpile of such quality, they threaten to stage more trophy bids across the board.
And that silverware, in turn, of course means a greater turnover in capital.
Shirt sales and merchandise withstanding, Rodriguez has shown that he has the ability to enact a new dynasty under Carlo Ancelotti, and his eagerness to represent Real's colours is very much enamouring, to boot.
The club are already enjoying a golden period in the wake of their European triumph, but Rodriguez's arrival could ensure that 2013-14 was just the tip of the iceberg.