United's last offer for the 2014 World Cup Golden Boot winner was thought to be in excess of 70 million pounds ($106.70 million), according to British media reports.
"I'm talking about figures which were very high indeed. If I were a bank manager then I would have had to accept it," Rummenigge was quoted as saying by the Manchester Evening News.
"But as a football club we allowed ourselves to close the door on it, and this door is remaining closed. I can promise that to everybody.
"But one thing is for certain, in view of the increased television money in England things are not going to get any easier for Bayern in future," he added.
Mueller has started the campaign in outstanding form, scoring five goals from the opening three league matches.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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