Rodriguez was sent on a two-year loan deal to the Allianz Arena last summer, at the end of which Bayern were expected to make his transfer permanent.
However, the resignation of Zinedine Zidane and arrival of Lopetegui had shifted the dynamic somewhat, with Rodriguez hungry to return to the Spanish capital and give himself a second chance.
That will have to wait 12 months though. As Marca reports, Rodriguez wants to honour his agreement with the German champions and repay the fans who have shown so much faith in him during his time in Bavaria.
Bayern are grateful for Rodriguez's loyalty but they are still hopeful of activating the purchase option in his contract next summer, which was the plan when the deal was originally struck.
That will depend on how Rodriguez fares over the next 12 months and if Real Madrid sign any replacements for him in the interim, as they know it will difficult to cancel his loan.
Even though the Colombian is still an employee of Real Madrid, his loan deal was effectively a probationary period before a permanent move and Los Blancos would have to spend a fee to bring Rodriguez back.
Lopetegui has turned Rodriguez's head by telling him that he wants him back in Spain, and the 27-year-old has made no secret of his sadness at leaving Real last year.
"It was sad and hard to leave," he said. "Real Madrid was always my dream. I always try to watch their matches at my house when I can."
However, he also said he was grateful for the "affection" of the Bayern supporters.