The Colombia international left the Bernabeu for a two-year loan spell with the Bavarian giants last summer after falling out of favour with previous manager Zinedine Zidane.
However, with the Frenchman no longer at the helm speculation has run rife over his return to the club a year earlier than expected following the appointment of Julen Lopetegui.
Earlier reports had suggested the 27-year-old was looking to make a return to Real next season with a clean slate, but the player's representatives Gestifute have told ESPN that a change in plans is not possible as neither club can break the agreement they struck last year.
Rodriguez will earn Real Madrid €5m in loan fees for each of his two seasons away from the club, although Bayern possess the option to make the deal a permanent one for €35.2m next summer.
The 27-year-old made 39 appearances for Bayern last term, notching eight goals and providing 14 assists as the German side secured their sixth successive league title in a campaign which also saw his current team knocked out by Real in the Champions League semi-finals on a 4-3 aggregate.
Rodriguez initially joined Real Madrid from Monaco following the 2014 World Cup in a deal worth €80m, where he went on to score 36 goals and set up another 39 across 111 appearances.
The Colombia international secured a La Liga title, Champions League crown and two Club World Cups with the Spanish giants prior to departing for his loan move.