A FIFA taskforce is currently studying the feasibility of moving the tournament in Qatar to the European winter due to fears about scorching summer temperatures in the Gulf state.
Such a move would cause significant disruption for European domestic leagues such as the Premier League and the Bundesliga, and Rummenigge is concerned that his organisation's 204 member clubs would pay the price.
"If now there is a strong wish (to move the 2022 World Cup) from various stakeholders like FIFA, UEFA, FIFPro and so on, we are ready to discuss, but under one condition: that there is no damage for club football," he told the Leaders Sport Business Summit at Chelsea's Stamford Bridge stadium in London.
"Because if we have a change from summer to November or to January, then they will be affecting our business, our calendar. And the bill at the end can't be paid by the clubs. We are not ready to pay such a bill.
"It has to be clear to FIFA and everybody who is now strongly involved in wishing to change the date that they need the goodwill of the clubs, otherwise we are not ready to talk and discuss about it."
ECA vice-chairman Umberto Gandini, an AC Milan director, proposed changing the dates of the 2022 Winter Olympics, which are due to take place in February of that year in either Beijing or the Kazakh capital Almaty.
"Not to be controversial, but the FIFA World Cup is one of the major events in the sports landscape, with the Summer Olympics," he said.
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"The Winter Olympics are not there, with all respect, as far as importance is concerned. But they are a very, very important event for the sport.
"If you are moving such a huge event like the World Cup from its natural window to winter, don't tell me that it's not possible to find a solution to move a little bit the Winter Olympics to avoid a clash.
"Especially when the Winter Olympics are still under the bidding process for 2022. There are two candidates at the moment, Beijing and Almaty, and no dates are set."
Rummenigge also said that Qatar could only be stripped of the tournament if American attorney Michael Garcia's recently completed report into corruption allegations surrounding the bidding process for the 2018 and 2022 World Cups produces evidence of wrongdoing.
"If the Garcia report is clean, it wouldn't be fair," the Bayern Munich chairman added.
"It's a decision that has to be respected by the football family."
FIFA president Sepp Blatter has said that the findings of Garcia's report will not be made public in order to honour promises made to witnesses.