The money, believed to be £4m plus interest, is understood to have been outstanding since Desmond bought the newspaper group, which publishes the Daily Express, Sunday Express and Daily Star, from Hollick last November for £125m.
Hollick, chairman of United Business Media, claims he is owed money from tax losses injected into the business, which is now part of Desmond's holding company, Northern & Shell.
Desmond's solicitors, SJ Berwin, said Hollick's claims were "without merit" and would be "opposed vigorously".
This is the second time Desmond's name has been through the courts in as many months. At the beginning of last month, Desmond lost a court battle with Daily Telegraph publisher Hollinger over the sale of their jointly owned West Ferry printing business.
Desmond alleged prejudicial behaviour against Hollinger and claimed directors of West Ferry had breached their fiduciary duty. Desmond's petition was thrown out of the High Court.
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