Rodriguez – nearing the end of a two-year loan spell at Bayern Munich – is a target for the Gunners ahead of next Thursday’s deadline.
Arsenal intermediaries have touched base with Real Madrid about signing the Colombia international.
According to The Independent, the Gunners fancy taking over Bayern Munich’s loan deal until the end of the season.
It is claimed the Bundesliga giants would be open to seeing Rodriguez leave for Arsenal.
While the 27-year-old is open to fighting for his future at the Bernabeu, he could be used as a makeweight to sign one of their top targets in the summer.
The Independent claim Bernabeu bosses would favour using Rodriguez as bait to sign Tottenham ace Christian Eriksen instead of selling him outright.
Meanwhile, Arsenal have announced transfer king pin Sven Mislintat will be leaving after the transfer window.
A statement from the club read: “Sven Mislintat, our Head of Recruitment, will be leaving us on February 8, 2019.
“Sven has been with us since December 1, 2017 and has done a truly outstanding job in helping us recruit players who are making a big impact now and will do so even more in the future.
“We wish him every success for the future and thank him for his extremely hard work on behalf of Arsenal.”
Mislintat added: “It’s been an amazing experience to work at a great club like Arsenal in what has been a big time of change.
“I am excited about what the future holds for the club and am looking forward to new challenges for myself.”