Transparency International, the anti-corruption campaign group, has also questioned why so few details have emerged about the reasons for the lifetime ban imposed on former FIFA presidential candidate Mohamed Bin Hammam.
FIFA general secretary Jerome Valcke has defended the world governing body, insisting it is down to the independent ethics committee - which has said it is looking into the World Cup bidding - to publicise any investigations.
Sylvia Schenk, Transparency International's senior advisor on sport who had worked with FIFA until cutting ties in 2011, said FIFA's credibility was at stake.
She said: "We are back to square one - we asked one and a half years ago for an independent investigation into all the allegations about the World Cup bidding and we still do not know what is going on.
"If the investigation into the awarding of World Cups in 2018 and 2022 is not transparent, few people will believe its outcome and FIFA will lose credibility."
Bin Hammam was banned in December by the ethics committee for life but the only reason given was for conflicts of interest while he was president of the Asian Football Confederation.
Schenk added: "No one knows what kind of conflict of interest we are talking about. Conflict of interest is usually viewed as less bad behaviour than corruption, yet Bin Hammam is banned for life while all the people charged with corruption by FIFA in 2010 received two or three-year bans.
"Lots of other people in FIFA have had allegations against them of conflict of interest but nothing has happened."
FIFA last year appointed US attorney Michael J Garcia as head of the investigations arm of the ethics committee, and German judge Hans-Joachim Eckert chairman of the adjudicatory arm.
Schenk claimed that Garcia could not be viewed as totally independent as he is paid by FIFA.
"We wanted an independent committee looking into the whole World Cup process - Garcia is paid by FIFA so is he all that independent?" she added.
She also criticised FIFA's new whistleblowers' hotline which feeds in directly to Garcia, saying any disclosures should be made to a fully independent body.
Valcke insisted it was up to Garcia to decide on any investigations and to publicise any details.
He said: "The chairman of the investigatory chamber can open an investigation whenever he wants, he doesn't need to receive any information from me.
"Whoever can provide him proof that something wrong happened during the bid process then he can open an investigation - it's his right.
"It's not up for me to say what he is doing. You have to talk to him, not to me. They are independent so I have nothing to do with it. Look at the ethics code - they are independent and they can do what they want."
Asked about the Bin Hammam ban, Valcke added: "I have no link to the investigation - you should ask the ethics committee directly."