Wright, who gained 25 caps for Scotland at prop forward and coached Glasgow Hawks up until a few weeks ago, had been tipped to take over from Tom Smith at Edinburgh having gained considerable experience with Scotland under-20s whom he will lead to a World Cup in South Africa this weekend.
Others believed to be in the running at Edinburgh include former Scotland forwards coach George Graham and Carl Hogg, who is to be interviewed for the position of Head Coach at the Gloucester club he currently serves.