While Arsenal manager Mikel Arteta is prioritising a new defender before the end of the January transfer window, speculation persists that a star name further up the pitch could make the move to the Emirates Stadium.
Despite featuring in Zinedine Zidane's plans earlier in the campaign, the Colombia international is now on the fringes of the squad, with Real keen to get him off the wage bill.
The 28-year-old has made 12 appearances in all competitions this season, although just one substitute outing has come since October 22.
However, with just six days to go until the turn of the month, Arsenal may have to move fast in order to complete what has the potential to be a complicated deal given the value and income of the player.
Here, Sports Mole predicts how Rodriguez could line up in the Gunners starting lineup should he move to North London.
Arguably the biggest quality of Rodriguez is his versatility, something which could benefit an attack like Arsenal who find themselves regularly having to use Pierre-Emerick Aubameyang on the left flank.
Should Rodriguez arrive in the coming days, top goalscorer Aubameyang would almost certainty switch to the centre, leaving Alexandre Lacazette to occupy a position on the substitutes' bench.
With Arteta seemingly intent on handing Mesut Ozil an opportunity to impress in the number 10 role, it would likely result in Rodriguez occupying one of the wings.
Nicolas Pepe has spent the first six months of his time at Arsenal on the right, contributing five goals and five assists from his 15 starts and 11 substitute appearances.
However, the Ivorian - and Arsenal - could potentially benefit from the 24-year-old switching to the opposite side, with the freedom to switch with Rodriguez on a regular basis during matches.
There is also the option of Ozil and Rodriguez being able to rotate between the left and centre, a scenario which would enable Pepe to continue on the right.
Either way, the arrival of Rodriguez would allow Arteta to present the trio with plenty of freedom, as long as the likes of Granit Xhaka and Lucas Torreira are prepared to stay in rigid defensive-midfield roles.