Speaking on Sky Sports FL Chairman Greg Clarke said "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.
"I wouldn't approve of any club taking on more obligations if they couldn't pay their existing ones."
The comments from the FL come after Cardiff pulled off one of the coups of the summer by signing Bellamy from the Premier League. Objections came initially from Motherwell - to whom City still owe money - and a good deal of the football media and opposing fans have been quick to have a dig at Cardiff.
A statement from Cardiff City has been reported on Wednesday evening and it reads:
"The club are fully aware of the comments made by Football League Chairman Greg Clarke on Wednesday. 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 has 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.
"By bringing Craig Bellamy to Cardiff City we continue to work in the interests of the club, the city and Wales. We will be in contact with the Football League on Thursday morning to discuss these matters further."
The monies owing to Motherwell, which promted the most incredible outburst from their chairman, "will be resolved within the next seven days", said Gethin Jenkins at the Bellamy press conference.