UEFA had 13 representatives at this year's World Cup, however, Platini feels that the record of European countries at recent tournaments is deserving of two additional places.
Each of the last three World Cups has ended with a European winner, with Germany claiming the title for a fourth time in Brazil last month following the triumphs of Italy in 2006 and Spain in 2010.
And Platini, who on Thursday announced that he would not run against incumbent Sepp Blatter for the FIFA presidency in 2015, is keen for the success of UEFA member nations to be rewarded.
"I have the intention to ask for one more [place] because we are world champion," Platini said.
"Now my job is to ask FIFA to come back to 15 [teams], in France in 98 we were 15, now we are 13 teams.
"We won the World Cup three times in a row, the quality of the world is with the European teams.
"I will go to the executive committee and ask for one team more."
