The case has been brought by Graham Power, deputy chief constable of Lothian and Borders Police. He claims he was passed over for promotion because he is English.
Mr Power, from Middlesbrough, was one of several leading candidates for the post of chief constable of the Northern Constabulary, which covers the Scottish highlands and islands. He was not, however, among officers shortlisted for interview.
He feels he was discriminated against because he was English. The joint police board which organised the selection process is challenging Mr Power's claim.
The legal argument must be settled before the full case can go ahead, but the result is unlikely to be announced today.