The Ibrox club has placed an advert in today's Financial Times newspaper.
The ad said the club was looking for "an exceptional business leader" who could "drive the club back to the pinnacle of Scottish and International sport".
Mather resigned as chief executive this month after replacing Charles Green who stood down in April over his alleged links to disgraced former owner Craig Whyte .
Earlier this week former Newcastle managing direction Derek Llambias ruled out taking up the role.
Llambias, who resigned from his position at Newcastle in June, said he did not want to return to a full-time position in football and feels Glasgow is too far away from his family home in London.
The post was advertised while the club is still yet to fix a date for it's AGM.
Its first annual general meeting on October 24 was postponed after a Court of Session judge ruled Rangers had to accept a resolution to appoint new directors to the board, which could not be circulated in time for the meeting date.
Rangers must stage an AGM by the end of December and must give shareholders at least 21 days' notice.
The club said it was working "as a matter of priority" to appoint new directors ahead of the AGM.