The star of the 2014 World Cup has found game time hard to come by under Niko Kovac at Bayern Munich, but his talent is known to everyone.
Under Jupp Heynckes in 2017/18, the Colombian was one of the stars of Bayern's team as they romped to yet another Bundesliga title.
For some reason and despite his struggles as boss, Kovac just isn't keen on the player who is currently on a two-year loan from Real Madrid.
Bayern paid £11.5m for the loan deal, with a £39.5m obligation-to-buy clause inserted.
However, the question on a lot of peoples lips is; how could the Gunners pull off the deal if he is still on loan at Bayern but registered to Real?
Well, it's all thanks to a rather obscure FIFA ruling, meaning that the deal is certainly a distinct possibility.
Article 5.3 in Fifa’s Regulations on the Status and Transfer states: "Players may be registered with a maximum of three clubs during one season. During this period, the player is only eligible to play official matches for two clubs.
"As an exception to this rule, a player moving between two clubs belonging to associations with overlapping seasons (i.e. start of the season in summer/autumn as opposed to winter/spring) may be eligible to play in official matches for a third club during the relevant season, provided he has fully complied with his contractual obligations towards his previous clubs.
"Equally, the provisions relating to the registration periods (article 6) as well as to the minimum length of a contract (article 18 paragraph 2) must be respected."
So if the Gunners can free up some wages - which may mean an exit for Mesut Ozil - and pay Bayern the £3m they want for the remainder of his loan, Rodriguez could be on the way to London.
It's been a tumultuous time for Arsenal and the fans of late, but at least there is some substance to the exciting links to Rodriguez.