The Turkey international has an expiring contract with his current club and appears to be on his way to Spain as German side have confirm the interest from abroad
A number of recent reports from Spain suggested that Madrid are in advanced talks with the Turkey international, and Rummenigge has now revealed that the Santiago Bernabeu side confirmed their desire to sign the 28-year-old.
"It is correct that Real Madrid are interested in signing Hamit Altintop. Our colleagues from Madrid have informed me about their interest, even though they are not obliged to do so," Rummenigge said to Welt Online.
"Hamit has played only three games from the start and that is not enough for him. We understand that and respect his decision. He told us that he did not want to extend his expiring contract with Bayern Munich."
Altintop is expected to conclude negotiations with Madrid in the upcoming weeks.