Rummenigge also defended Bayern, adding: "I have to say that, from our point of view, there are no irritations".
The 46-year-old Kovac took over at the "Eagles" in March 2016 and led the club out of the Bundesliga doldrums.
Frankfurt's sporting director Fredi Bobic was furious, accusing Bayern of being "not professional and disrespectful". Both of us and Hasan [Salihamidzic] have tried for a very, very long time to persuade Jupp.
Bobic accused the Bundesliga champions of leaking news of their agreement with Kovac prior to Friday's confirmation of his installation as coach starting next season. With that said, he will be able to play against his old team, as UEFA don't allow clauses that prevent players out on loan to play against their employees, although they're quite common when players are loaned out to league rivals.
He said at a press conference on Friday: "The offer has surprised us at this stage of the season, but we owe a lot to Kovac". "They did their thing and thought of themselves".
"He's a young coach and he has done well at Eintracht Frankfurt", enthused the Colombian, who top-scored at the 2014 World Cup with six goals.
'Kovac generally makes a very positive impression, ' Heynckes said. "Not of Eintracht Frankfurt".
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Frankfurt can still win a title this season as Kovac's men clash with Schalke in the German Cup semi finals on Wednesday.
And Rodriguez is looking forward to lining up against Real in the Champions League last four.
Former Croatia global Kovac, who has signed a three-year contract, claims the whole deal was done on Thursday.
"The coach keeps the team together brilliantly".
"When we realised in a final, final conversation that he was not doing it, we were talking to the coach, who was free, Thomas Tuchel".
While Kovac's hopes of guiding his current club to Champions League qualification suffered a significant setback in a 4-1 loss at Bayer Leverkusen on Saturday, Bayern had no such problems as they cruised to a 5-1 hammering of Borussia Monchengladbach.
Kovac will need to adjust to instructing established stars at Bayern, rather than young players of promise still eager to learn, and he will be expected to maintain the club's high standards.