Rummenigge told Germany's Sky Sport: "Actually, the conversations Hasan had with him were always very productive. And at some point it actually seemed that [a deal would be reached]. But then Thiago informed Hasan that he would like to do something new again, and so it is.
"We will have to accept that. We have a contract that is still valid for one year and if he agrees with any club and that club should pay a transfer of a certain amount.
"I don't want to make any public comment about the amount that we have in mind. Then we will deal with it, but we will not, as I have already said, hold a summer sale.
"I'm not angry at all, I like him. I think he's a great footballer, a fine footballer and he's a good character too. And one shouldn't forget either: At 29, he is at an age where, if he wants to do something new, he has to do it now because if you are in your 30s, it will be more difficult to make transfers."
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Rummenigge was circumspect on the impact of coronavirus on club finances, and expects transfer fees to drop during this window.
"I think I have a very good network with many colleagues - regardless of whether it is Real Madrid, Barcelona, many English clubs, France, Italy - and I can say very clearly: Everyone groans, everyone suffers. Everyone has reduced income," he explained.
"I can also say one thing: the bigger clubs have bigger revenue reductions than the smaller ones. Of course, that is in the nature of things, because of course the income is also a bit more questionable for all of us and we used to have higher income."