Ronaldo, 32, appears to be heading for the Real Madrid exit this summer following a high-profile tax dispute, and it had been claimed that Bayern were preparing to pursue the Portugal captain ahead of the 2017-18 campaign.
Rummenigge, however, has called the rumour "complete unfounded", and insisted that such talk "must be consigned to the realms of fantasy".
"We're used to being the subject of intense transfer speculation during transfer windows," Rummenigge told Bayern's official website.
"Normally we don't comment on rumours, but in this case, we would like to make our position on Cristiano Ronaldo absolutely clear: This rumour is completely unfounded and must be consigned to the realms of fantasy."
Ronaldo, who is currently with the Portugal squad at the Confederations Cup, is said to be desperate to return to former club Manchester United in this summer's transfer window.