Robertson also explained some of the characteristics the Rangers board will want the new manager to possess.
“I think we need a strong character, with a strong mentality,” he added to the Rangers site. “Someone who understands and gets what Rangers is all about.
“Whoever comes in is going to get the backing, there will be financial resources in terms of taking the club forward.
“But most of all we need someone who is a winner and someone who gets what this is all about and what Rangers is all about, which is winning. We are looking for the highest calibre possible, a club of this standing deserves the highest quality of manager.
“We need someone with character and someone who can work under the pressures that they will face working at Rangers.”
Robertson made it clear that a technical director will be appointed to take charge of recruitment in what appears to be a departure from the system in which McParland was in charge of transfers.
Rangers chairman Dave King was highly critical of the club’s recruitment last summer when the board were persuaded by Warburton to buy 11 new players rather than the five to six they had initially planned.
Joey Barton, Nico Kranjcar, Philippe Senderos and Jordan Rossiter were among the flop signings brought in by the McParland and company.