"The best thing would be to hold a rebid for the World Cup tournaments for 2018 and 2022," Collins said during a meeting dedicated to the relationship between Great Britain and FIFA.
In late May, several FIFA officials were arrested in Switzerland under a US anti-corruption warrant as a total of 14 world football figures were indicted by the US Justice Department on charges of money laundering, wire fraud and racketeering. FIFA President Joseph Blatter announced his resignation just four days after he was reelected as the head of the football association.
Swiss authorities have launched a separate investigation into the selection process of World Cup host countries, particularly Russia in 2018 and Qatar in 2022.
FIFA's compliance chief Domenico Scala told Swiss media on Sunday that the two tournaments could be annulled should evidence emerge of alleged bribery surrounding the selection process. So far, the evidence has not been provided, Scala said.
Both Russia and Qatar have denied any wrongdoing in the World Cup bidding process.
On Monday, FIFA said in a statement that Russia's and Qatar's hosting rights for the 2018 and 2022 World Cups have "no legal grounds" to be annulled.
