Europe currently provides 13 of the 32 teams at the finals, compared with five from Africa and four or five, depending on the winners of a playoff against a South American team, for the most populous continent Asia.
FIFA President Sepp Blatter wrote last week that Africa and Asia deserved more representation at the showpiece event because they had more member associations than Europe and South America.
Former France international Platini, widely regarded as the most likely successor to Swiss Blatter in the FIFA job, said by his own calculations that adding eight more teams would require extending the tournament by only three days.
"It's good for everybody," Platini told the Times newspaper in an interview.
"I totally agree with Mr Blatter that we need more African and Asian (teams). But instead of taking away some European, we have to go to 40 teams.
"We can add two African, two Asiatic, two American, one Oceania and one from Europe."
European and South American countries have won all 19 versions of the World Cup.