Arsene Wenger, FIFA's chief of Global Football Development, has been promoting the idea as part of the organisation's review of the international match calendar and this week repeated his support for the change from the established four year cycle, Reuters reported.
But European football sources told Reuters that any attempt by FIFA to introduce such a change would face resistance from European governing body UEFA, the European Club Association (ECA) and is unlikely to win the backing of the major domestic leagues.
Responding to a letter to a fans group Football Supporters Europe, UEFA president Aleksandr Ceferin said there were "concerns across the footballing world" about the plans being put forward by the former Arsenal manager.
"Considering the major impact this reform may have on the whole organisation of football there is widespread astonishment that FIFA appears to be launching a PR campaign to push its proposal whilst any such proposals haven’t been presented to confederations, national associations, leagues, clubs, players, coaches, clubs and all the football community," Ceferin wrote in the letter on Friday, a copy of which has been seen by Reuters.
"As one concrete example amongst so many, it is imperative to highlight the concerns shared across the footballing world regarding the impact a biennial FIFA World Cup would have on the international match calendar and, prominently in this context, on women's football," he said.
Wenger's plan is for a World Cup to be followed the next year by continental championships, such as the Euros and Copa America, which would mean no summer clear for the women's World Cup and their continental tournaments.
"UEFA and its national associations... have serious reservations and grave concerns surrounding reports of FIFA's plans," Ceferin added.
FIFA said that a consultation on the proposal is ongoing and will continue over the coming months with all key stakeholders, including confederations and member associations.