Liverpool, Arsenal, Juventus, Napoli and Inter Milan are also reported to be interested in the 27-year-old, who can operate as an attacking midfielder or as a winger.
The Colombia international joined Bayern on a two-year loan deal from Madrid in the summer of 2017.
With no Champions League football, Everton may not be too enticing for Rodriguez, who has regularly feature in Europe’s premier club competition with FC Porto, AS Monaco, Madrid and Bayern.
Moreover, the 27-year-old is used to challenging for major titles and winning them, and Everton will be a step-down for him.
However, for Everton, securing the services of Rodriguez will be a massive coup and will make the rest of the clubs in the Premier League sit up and take notice.
The Colombian is a very good attacking midfielder with a superb left football, and the Madrid-owned star will instantly make Everton a potent force in attack.
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