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Chairman Greg Dyke has insisted the Football Association will not let FIFA off the hook, but expects it to take time before it gets answers.
The FA has issued a list of questions to FIFA following Sepp Blatter's revelation a deal had been fixed to hand Russia the 2018 World Cup before the vote.
The FA spent ?21million on a bid for the tournament, but outgoing FIFA president Blatter disclosed last month an agreement had been made by senior figures in the organisation for the event to go to Russia. England secured just one vote, apart from its own, in December 2010.
Dyke doubts the FA's issues will be resolved by FIFA's first reply, but says the organisation is prepared to wait.
"Do you mean answered, or answered satisfactorily?" he said, when asked when he expects to hear from FIFA. "I think we'll get an early answer quickly but with that we'll then go back to our barrister.
"A lot of people put in money - I believe Birmingham City Council put in ?250,00, for instance - so when all that stuff came out from Blatter, we said 'Let's go and talk to our lawyers' because we needed to work out what the legal basis for getting our money back was, if you can, and we went to a QC.
"They suggested we ask FIFA a series of important questions. Our intent is to get the ?20-odd million back, from FIFA. They've got the questions, yes. We want answers back before we lodge our claim.
"If it can be proved what Mr Blatter said is true, that it was sorted out before they ever looked at our bid then yes please, we'd like our money back."
Dyke questioned on Monday whether any World Cup bid had been won without "a pile of bungs" following Wolfgang Niersbach's resignation as president of the German football association (DFB).
Niersbach, who will stay on FIFA's executive committee, stepped down amid an investigation into allegations corrupt payments were made to officials during the bidding process for the 2006 World Cup, which was staged in Germany. He denies any wrongdoing but said he took the decision to quit in order to "protect the DFB".
Meanwhile, Dyke confirmed the FA's investigation into independent board member Heather Rabbatts is likely to be completed before the end of the month.
Rabbatts is facing a complaint for alleged breach of the FA's code of conduct after her public backing for the former Chelsea doctor Eva Carneiro.
She expressed what she called major concerns about the FA's disciplinary process that cleared Jose Mourinho of making discriminatory comments towards the doctor.
Dyke added: "We are quite close to finishing that."