Clarke warned that the League may not register Bellamy, on a season loan from Manchester City, without assurances.
Cardiff have debts estimated at £30m and have missed tax bill deadlines.
"Our job is to make sure there is an integrity of competition, that people don't take on liabilities they cannot meet," Clarke told Sky Sports.
"We have asked Cardiff City for certain information, which will remain confidential between them and us, which will enable us to appraise whether we register the player or not."
Cardiff issued a statement on Wednesday night, promising to take up the matter with the Football League at the first opportunity.
"The club are aware of the comments made by the chairman of the Football League," said the Cardiff statement.
"We are disappointed that he's chosen to discuss these matters in public and will be in contact with the Football League on Thursday morning."
Cardiff still owe Motherwell £175,000 for the transfer of Paul Quinn in July 2009 and the Scottish club's chief executive, Leeann Dempster, has been publically critical of Cardiff's recent signings.
"They [Cardiff] have signed a high-profile player, which has really annoyed us," Dempster said this week. "They should have their debts settled from last year before they are allowed to sign any players."
As well as the surprise capture of Bellamy, midfielders Jason Koumas, Seyi Olofinjana and Danny Drinkwater have all arrived for the season from Premier League teams.
It is thought that Manchester City will continue to pay the bulk of Bellamy's wages, but Cardiff's combined wage bill for their new recruits will still be significant.
Cardiff chief executive Gethin Jenkins has promised Motherwell that their situation "will be resolved within the next seven days".
Jenkins has also pointed out that increased ticket sales and merchandising sparked by Bellamy's signing on Tuesday will have a beneficial effect on the Championship club's finances.
Source: BBC Sport
Source: BBC Sport