"There are huge bribes" in the world football governing body, UAE-based Maradona told Abu Dhabi daily, Al-Ittihad.
"Those behind them must be held accountable, especially in regards to the latest events related to awarding Qatar the 2022 World Cup.
"Where has this money gone, who received it, and why," must all be investigated, he said, adding that he had repeatedly denounced, "in vain, cases of bribery within FIFA."
Qatar is facing growing pressure over its hosting of the 2022 World Cup after fresh allegations over the role disgraced former top football official Mohammed bin Hammam played in its bid.
Last week, Britain's Sunday Times newspaper said it had obtained millions of emails, documents and bank transfers showing that bin Hammam paid over $5 million (3.67m euros) from slush funds to win support in the bidding process.
FIFA completes its probe Monday into the 2018 and 2022 World Cup bids, won by Russia and Qatar, chaired by former US attorney Michael Garcia.
"I hope football would go back to being a fun game away from bribery and corruption," said Maradona, who will be present at the World Cup in Brazil as a commentator for a Venezuelan television channel.
"It is unfortunate that there are footballers within FIFA such as (UEFA president Michel) Platini, who have surrendered" to such irregularities, he said.
Platini has attacked The Sunday Times for seeking to "tarnish" his reputation by drawing him into the corruption claims against the Qatar World Cup bid.
The Qatar 2022 Supreme Committee for Delivery and Legacy has repeatedly denied any wrong-doing.
The choice of Qatar to host the 2022 World Cup shocked many observers due to its searing heat in the summer.