Uefa secretary general Gianni Infantino told reporters in Vienna that the governing body felt it deserved 14 places in the Fifa World Cup.
Uefa was allocated 13 slots at the 2014 World Cup in Brazil and wants a 14th next time around, in addition to Russia who qualify automatically as hosts.
"I think there is a big chance that we will have more than 13 because if you look at it objectively, based on facts, 19 of the top 32-ranked associations are European," Infantino told reporters.
"The winners of the last three World Cups were three (different) European teams, so I think it's absolutely objective and fair to be asking for one more place only."
"We could ask for more than one (extra), but one would already be a good sign that... at the end of the day, to crown the world champions you must have the best teams."
Fifa's executive committee will hold an extraordinary meeting on 30 May to decide how many places each continent will get at the World Cup.
Infantino went on assess other continents.
"I think that South America also deserves the number of teams that they have in the competition," he said. "You can argue whichever way you want but there are facts and at the end football is not like the Olympic Games where the importance is to participate. In football the importance is to win so it is about sporting results and the sporting results are clearly for Europe whichever way you turn it and whichever way you argue it."