The Sport titles were printed by Desmond's company Northern and Shell, which owns Daily Star and Daily Star on Sunday, former rivals of the now shut Sport titles.
Print bosses at Desmond's company would not give details of the amount owed by SMG but said "they do owe us some money".
"Northern and Shell was one of a number of creditors to which SMG owed money. They were, however, a pivotal creditor as their services were required by Sports Media Group on a daily basis," a spokesperson for administrators BDO told Journalism.co.uk.
Administrators for Sport Media Group (SMG) were unable to say whether the debt to Desmond's firm was a contributing factor in the closure of the Sport titles.
A statement on the SMG's website confirms the Sport titles ceased trading because of its "inability to meet certain creditors as they fall due".
The last accounts filed by SMG, which are for 2009, show debts of £11.9 million to the Royal Bank of Scotland, which includes loans and credit facilities.
Desmond may have lost money in the Sport's collapse and the loss of a printing contract, but he is likely to have inherited readers from his former rival.
Northern & Shell sister paper the Daily Star Sunday has welcomed former Sunday Sport readers the previous two weekends using the Sport masthead (pictured).
Barclays Capital has made a prediction that the four national newspapers owned by Desmond will see an almost doubling in profits over the next two years, which could entice potential bidders for the Daily Express, Sunday Express, Daily Star and Daily Star Sunday, according to the Guardian.
Founder of the Sport titles and former owner David Sullivan, who bailed the company out in 2009, with a £1.6 million loan, did not offer more money to save the titles this month, administrators told Journalism.co.uk.
Sullivan, who is joint chairman of West Ham United, launched the Sunday Sport in 1986, and the Daily Sport in 1991, and sold them in 2007 for £40 million. The day before the Sport titles ceased publication SMG's share price fell and the company was valued at less than £1 million.
The last ABC certificate for the Daily Sport was registered in January 2009, and showed the paper had a circulation of 72,592 copies. The company pulled its titles from ABC in March 2009.
Administrators were unable to release a list of creditors or the amounts owed and said they are negotiating with interested parties in buying the Sport titles.
If no deal is done the loss of the Manchester-based Daily Sport will be the first national daily to shut since Today in 1995 and the last national newspaper produced outside of London.