It was presumed that Gray would take the required coaching exams to qualify him to manage in the Premiership next season should The Whites avoid the drop.
However, Richmond says there is insufficient time for him to obtain the qualifications he will need.
Richmond said: "Eddie will remain at Leeds United in an important capacity, but if we stay in the Premiership it is impossible for him to be the manager because it is not possible to get a coaching badge in one season. It takes longer than that."
Gray has special dispensation from the Premier League to remain in temporary charge until the end of this campaign.