Bayern President Uli Hoeness has pledged a big-name signing in the close season and Italian media had reported in recent days the German champions were interested in Ronaldo.
"We are used to a lot of speculation about possible comings and goings during the transfer period," said Rummenigge in a club statement with the headline "Hoax of the Day for the Ronaldo rumours".
"As a rule we do not comment on these rumours but now in the case of Cristiano Ronaldo we want to make it clear once and for all that this rumour lacks any foundation and must be confined to the real of fables."
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Ronaldo is seen as likely to leave Spain despite winning the Champions League for a second season in a row with Real following accusations of tax fraud in the country.
According to reports in Portuguese media, the 32-year-old four-times world player of the year had already made up his mind to ask the club for a transfer, saying he was "deeply disenchanted" with the allegations against him.
Spanish prosecutors have filed a lawsuit against the player accusing him of defrauding tax authorities of 14.7 million euros ($16.5 million) by hiding his image rights income between 2011 and 2014. Ronaldo has denied any wrongdoing.
(Reporting by Karolos Grohmann; Editing by Alison Williams)
