The Gunners are looking into the possibility of signing the Colombian attacker in the summer, if not this month.
James Rodriguez is currently on loan at Bayern Munich from Real Madrid, who are searching for potential suitors for the midfielder in the summer.
One of those suitors is Arsenal, who have contacted the Spanish club about a possible deal, according to Miguel Delaney of the Independent.
The North London club are apparently looking to bring Rodriguez in on a short-term loan with a view to making the deal permanent in the summer, a situation that would suit all parties.
There is one wrinkle in this possibility, however – Madrid want to sign either one of Christian Eriksen or Eden Hazard, and if it is the former, then the reigning Champions League winners are open to sending James to Tottenham Hotspur as a makeweight.
It would be hugely ironic for Arsenal to miss out on a highly desirable target to their arch rivals, but manager Unai Emery has said that he is open to any deals that will “help” the team.