Bellamy is being reported as earning £90k a week and the Football League have asked Cardiff to show they have the necessary fund with Greg Clarke of the Football League saying to the BBC: "Our job is to make sure there is an integrity of competition, which people only take on liabilities that they can meet.
"We have to register the player and we've asked Cardiff for some information, which will be confidential between them and us, which will allow us to appraise whether we are going to register that player or not.
"Without pointing the finger directly at Cardiff, I have an abiding principle that people in business and their personal lives should always pay their debts.
"It depends what money they've got available and it depends whether they intend to take on an obligation and extinguish their other obligations at the same time.
"I don't know the answers to that, but we'll find out the answers. But certainly I wouldn't approve of any club taking on more obligations if they couldn't pay their existing ones."
Cardiff last night issued a statement saying:
"The club are fully aware of the comments made by Football League chairman Greg Clarke on Wednesday," said the Cardiff statement.
"We are extremely disappointed that he has chosen to discuss these matters in public without waiting for an opportunity for Cardiff City to provide a full and private response.
"As we have stated previously, we are fully confident that this deal adds up in a business and sports context.
"It should be remembered that the club have released 10 players this summer and to date have brought in two free agents and season-long loan players.
"We are extremely proud to have reached a sensible deal with Manchester City which has allowed us to bring Craig home to realise his dream of playing for his home-town club and to help us pursue our ambition of challenging to join the Premier League.
"This deal has also been fully supported and underwritten by our Malaysian investors who have shown unprecedented support since joining the club.
"We will be in contact with the Football League on Thursday morning to discuss these matters further."