Having spent the last two seasons on loan in Bavaria, Bayern could have triggered a deal to sign him permanently for €42 million (£37m/$47m).
But the Colombia international has told the club he does not intend to stay, leaving his immediate future now up in the air.
Rodriguez scored 15 goals from midfield in two seasons at Bayern, and was named in the Bundesliga Team of the Season and Champions League Squad of the Season in his first campaign.
There had been some suggestion that Bayern could exercise their option to buy Rodriguez before selling him on at a higher price, but Rummenigge would not consider such an idea .
“That would not be fair to Real Madrid and not the style of Bayern, we do not engage in trafficking here,” he said, adding that he will personally regret Rodriguez’s departure.
What the future holds for Rodriguez now is unclear. Turning 28 this summer, he is no longer world football’s golden boy and it seems unlikely that he will remain at Real Madrid.
Rumours have suggested that he could be used in a swap deal as Madrid look to offset some of the costs of their planned summer revamp.
That could mean a move to the Premier League – Madrid are thought to be interested in a move for Paul Pogba, though more concrete interest from Juventus could make such a deal unlikely.
Despite shining for his country with 22 goals in 69 caps, he has never reached a major international final.
To date, his best showing has been the third-place finish Colombia achieved at the 2016 edition of the Copa America, where they were beaten by eventual winners Chile.