FIFA president Sepp Blatter tendered his resignation on June 2 despite winning an historic fifth term after a series of scandals rocked the organisation.
Football’s governing body was plunged into crisis at the end of May when 14 current or former FIFA officials and sports marketing executives were charged in Zurich as part of a US investigation into alleged corruption.
FIFA Secretary General Jerome Valcke said on Wednesday that FIFA would postpone the bidding process for the 2026 World Cup, as investigations continue into allegations that bribery helped determine the hosts of earlier competitions.
Swiss authorities have opened a separate investigation into how the 2018 and 2022 World Cups were awarded to Russia and Qatar respectively.
Boyce, whose four-year reign as home nations vice president came to an end last month, welcomes the investigations and hopes anyone convicted of wrongdoing is severely punished.
“Quite honestly, once again it is dragging the game we all love through the mud,” Boyce told Sky Sports News HQ.
“It is despicable for want of a better word but, having said that, I welcome the investigations that are being carried out both by the FBI and the Swiss authorities.
“I have made it abundantly clear that following these investigations, if anyone is found guilty of dishonesty or corruption, I hope they are dealt with in the strongest possible manner.
Boyce added: “If there is undoubtedly proof that corruption was involved in the bids for both Russia and Qatar then I personally feel the executive committee and the new president, when he is elected, need to look at having a revote.”
Though Blatter has tendered his resignation it is currently not scheduled to take effect until December at the earliest.
Boyce, who has known Blatter for over 20 years, believes the 79-year-old should leave his post as soon as possible for the good of the game.
“He has now decided that he is going to step down as president of FIFA,” Boyce said.
“I have always said I do not have a problem with Sepp Blatter from a personal point of view but I think probably in the interests of FIFA – now that he has made that decision – the sooner a replacement is elected, the better.”