The case is listed before the Commercial Court on Monday.
Holtglen Ltd, which built a shopping centre in Kilkenny in which Dunnes agreed to be the anchor tenant, has brought the petition following Dunnes' failure to pay after being ordered to do so by Mr Justice Peter Kelly in a summary judgment order issued last March.
The Ferrybank shopping centre was completed in 2009 but Holtglen later became insolvent and its Bank of Ireland loans were transferred to NAMA company, National Assets Management Ltd.
It is understood NAMA wrote to Dunnes on October 30 warning that unless Dunnes paid some €21.6m (the €20.4m judgment sum plus interest) within seven days, Holtglen would proceed to publish a petition to wind up Dunnes on grounds it is unable to pay its debts and/or it is just and equitable that it be wound up.
Last March, Mr Justice Kelly granted summary judgment for some €20.4m to Holtglen against Dunnes after he dismissed Dunnes' application to set aside an arbitrator's award for €20.2m to Holtglen arising from an agreement to build the centre. Holtglen claims, despite the summary judgment order, Dunnes has still not paid and now owes it some €21.6m.
Last September, it served a notice on Dunnes under Section 214 of the Companies Actwhich provides, where judgment has been obtained against a limited company, a notice can be issued threatening to wind up that company.
If the debt is not paid within 21 days, a petition can be presented to the court seeking to have the company wound up.
On November 9, a petition was issued and the matter is due before the Commercial Court on Monday.
Previously, the Commercial Court heard Dunnes had instituted arbitration proceedings claiming breaches of a development agreement by Holtglen which in turn counterclaimed for payment. Holtglen claimed it was then entitled to stage payments due under the development agreement, plus other sums for which it had counterclaimed.
It said it has very large borrowings in connection with the Ferrybank development and it was "of the utmost importance" it was paid by Dunnes as soon as possible. Holtglen later became insolvent.
In October 2011, the arbitrator, while upholding some of Dunnes complaints of breaches of the development agreement, found Holtglen had remedied those matters and Dunnes was not entitled to terminate the development agreement.