The club are demanding details on the exact identity of the corporation before handing over £5.75m, which was due last Friday.
Club president and former owner Sam Hammam has been widely seen as Langston's representative.
Chairman Mehmet Dalman said: "It is bad governance not knowing who is the owner of a debt we are trying to honour."
He added: "Right now I want to know who it is."
Dalman said former owner Hammam had told the club he was "not" a representative of Langston.
The original debt of £24m was in the form of loan notes issued by The Langston Corporation when Hammam was at the helm of the club.
In 2013 Cardiff and Langston announced "an amicable resolution" to the longstanding debt issue.
Hammam became life president of the club as part of the settlement and his representative Michael Filiou also took a seat on the board of directors.
"Michael Filiou represents Langston on the board, but he cannot tell us who he represents," said Dalman.
http://www.bbc.co.uk/sport/0/football/31040542