The Dutch-born Coolen was removed as United's coach in December 2011, just 18 months into a four-year contract.
United removed Coolen from the coaching role and told him to head the club's youth development program.
Coolen has sued United, seeking damages over the termination of his contract worth $275,000 a year plus benefits, while the club maintains it acted within its rights.
The South Australian District Court began hearing legal argument on Monday's opening day of the trial before Judge Geoffrey Muecke.