"If I find the opportunity, I will offer them Islam with ease and grace, and if I do not find the opportunity, I will tell them that you are our guests and our brothers in humanity."
But he stressed that Islam does not accept conversion through coercion.
Social media posts have claimed that hundreds of fans have changed faith but AFP's fact-checking service has shown those claims are fake.
An official at Qatar's ministry of religious endowments told AFP that the goal of the state was not "the number of converts to Islam, but rather the number of those who change their opinion about it."
Fans said they found the idea of World Cup conversions absurd.
"It is a good opportunity to learn more about Islam," said Petr Lulic, a 21-year-old Croatian in Qatar with his family. "But no one embraces a new religion during a football tournament."