Rummenigge, who is also chairman of the 207-member European Club Association that lobbies for the rights of European clubs, told France Football magazine that it made no sense that European clubs played in mid-winter.
"Everywhere, be it Germany, France or England, summer is the best period of the year. And that is the season we don't play," Rummenigge said. "In deepest winter, when it is very cold and snowing, we play nearly all the time in conditions that are disagreeable for both players and spectators. It is not logical."
Rummenigge said Fifa and Uefa were "seriously thinking" about an overhaul of the soccer calendar so European leagues would open in January and wrap up at the end of autumn.
"My sense is that we are heading straight in this direction," the former West Germany international was quoted as saying of possible January-autumn European leagues.
Asked whether soccer's traditional summer break could be abandoned, Rummenigge replied: "It's completely possible, even if this idea does not thrill our friends in South America."
ECA vice chairman Umberto Gandini was not aware of the plan. "That was a really nice surprise ... he is not reflecting the position of the ECA," Gandini said.
A sweeping overhaul of league and international schedules for the world's most popular sport would likely be far more complex than Rummenigge's comments suggested, perhaps impossible.
The suggestion that club soccer could monopolise the calendar and that Fifa's principal source of income, the World Cup, and Uefa's European Championship could be tacked on at the end of the year, when club soccer is finished, won't likely thrill officials at either of those governing bodies.
There are also major financial, broadcasting, geographical, sporting and cultural obstacles to any drastic overhaul - not least the issue of whether Europeans would attend and watch soccer in summer months when many of them traditionally sun themselves on beaches.
Rummenigge told France Football that one "advantage" of modifying the calendar would be that club and international soccer could be separated entirely so players aren't called up by their countries when their clubs are still playing.
"In future, there could be two phases: one for club competitions, the other for qualifying matches or finals of the World Cup or the Euros," he said. "For one month, national teams would be completely free to call up their players."
Fifa's plans for the 2022 World Cup to be held in host Qatar's scorching summer months are also feeding debate about soccer's international calendar. Some in soccer, including Uefa president Michel Platini, have appealed for the flagship tournament to be moved to the Gulf state's somewhat cooler winter months. But that could punch a hole in the European club season as it now stands.
The English Premier League said a winter World Cup in 2022 "is unworkable and unacceptable to domestic European football".
Rummenigge suggested that any change in scheduling for Qatar could be used to make permanent changes to soccer's calendar.
"It is clear that there will soon be negotiations to examine what can be done. My point of view is that an eventual change to the calendar shouldn't be viewed critically but more as an innovation that could improve the general context," Rummenigge said. "Changing the calendar carries risks but it is also an opportunity. The issue of the calendar will become more important the closer 2022 gets."
You could imagine the outcry from the Cricket lobby in England if this became a reality!