The announcement marks a new development in what has been a prolonged fall-out to the decision to award the tournament to Qatar, although UEFA are not ready for FIFA to make a decision on exactly when the competition will be played, with a switch to January 2022 or November and December in the same year both said to be under consideration.
FIFA are thought to prefer a tournament in November and December to avoid a clash with the Winter Olympics, and the executive committee is expected to agree in principle to reschedule the event at their meeting in Zurich at the start of next month.
Qatar's position as host of the event has long been a subject of controversy, with many questioning the country's suitability due to the extreme temperatures in the Middle Eastern nation during the months in which the competition usually takes place.
FIFA president Sepp Blatter and his UEFA counterpart Michel Platini have both indicated that rescheduling the tournament is a plausible solution.
And the proposal now appears to be gathering pace after the associations that make up European football's governing body pledged their support at a meeting in Dubrovnik, Croatia.
"Obviously there were certain reservations regarding the World Cup in Qatar," FIFA vice-president Jim Boyce told SkySports News.
"But everyone agreed it would be impossible to play a World Cup in the severe heat of Qatar in the summer.
"What the 54 countries do not want FIFA to do is to make a decision yet on exactly when in the year it is going to be played.
"It's wrong to speculate at the moment when this is going to be played. The stakeholders need to sit down and come up with the best solution.
"The most important thing is that we have a World Cup that people can go to and enjoy."
