LEXINGTON, Ky. (AP) — The University of Kentucky countersued fired men’s basketball coach Billy Gillispie on Thursday, claiming it doesn’t owe him pay because he never signed a contract.

The employment dispute escalated when the university filed a lawsuit in Franklin Circuit Court in Kentucky, one day after Gillispie filed his own claim in Dallas, asking for $6 million in lost salary and undisclosed punitive damages, attorneys’ fees and court costs.

Gillispie, who was fired March 27, was working under a seven-year memorandum of understanding but hadn’t signed a formal contract during the two years he coached the Wildcats.

A call to Gillispie’s attorney, Demetrios Anaipakos, was not immediately returned.

UK’s lawyers are asking the court to rule that the two-page memorandum of understanding Gillispie signed after his hiring in 2007 was not the equivalent of a full contract. Gillispie says it is and that he is entitled to $1.5 million a year for four of the five years left on the deal.

‘‘UK contends that the (memorandum of understanding) is not an enforceable long-term contract of employment, and that it owes no damages to Gillispie, having paid him for each basketball season in which he coached,’’ the lawsuit says.