The 15-year-old, regarded as one of the country’s most promising talents, will be free to leave Rangers on his 16th birthday in June. It is understood a fee of around £600,000 has been negotiated between Rangers and Chelsea if Gilmour decides he wants to move to the English Premier League club.
If the Ayrshire-born player was to move on after his 16th birthday without a deal in place, Rangers could only expect to receive training compensation of around £100,000.
New Rangers manager Pedro Caixinha is making efforts to convince Gilmour to continue his development at Ibrox, where he is already considered to be close to first team recognition.
SFA performance director Malky Mackay has also expressed the view that Gilmour would be best advised to stay with Rangers, rather than run the risk of slipping into obscurity in the academy system of a major English Premier League club.
Robertson said: “We would love Billy Gilmour to stay but we need to protect our position and do the sensible thing,” said Robertson.
“If he goes in the summer without a deal being agreed then he leaves only for a compensation amount.
“That would be a hell of a lot less than if we had a fee agreed beforehand. We have protected our position on that side of things but we’d like Billy to stay at the club.
“Everybody on the football side thinks he’s a fantastic talent and he’s still only 15.
“It would be great to see a boy like that develop and stay here to get a lot of game time and go further. Malky Mackay has also questioned if we really want to see him get lost in a big academy. I hope not because he would certainly be looked after here and be given an opportunity.
“I think there’s a reasonable chance he could stay – we’ve done all we can. We’ve tried to sell Rangers and the opportunities to him in the best possible way on the basis of his career going forward. We’d give him a platform to go forward. If there are other big clubs interested, then we’re all human and his head could be turned. But we believe we could give him a platform to have a terrific career.
“We have got a position agreed if he was to go. I won’t tell you the number but there is a position agreed. It would be negligent of us not to have done that in terms of the governance of the club, but we’d rather not get the money and Billy stayed and went on to have a great career at Rangers.”
It has been speculated Chelsea may look to immediately loan Gilmour back to Rangers but Robertson insists that has not formed part of any agreement struck so far.
“It’s not been discussed,” he added. “It’s possibly an opportunity but we’d just rather he stayed here, to be honest. I don’t know for sure when a decision will be made. Hopefully sooner rather than later because then everyone knows where they’re going. He’s under contract until he is 16 in June. Ultimately in that situation the player has the power to some extent. There is only so much you can do. You put your best foot forward and we’ve done that.”
Robertson, speaking at the launch of Rangers’ new Community Engagement initiative, also provided an update on the club’s search for a Director of Football and Caixinha’s recruitment of a Rangers-connected addition to his coaching staff.
“I know there was talk of the director of football appointment being ‘imminent’ but that’s imminent in the grand scheme of things, not as in tomorrow,” said Robertson. “I won’t put a timeframe on it but we are applying some brainpower to that again.
“There has been a bit of confusion about what a director of football will do but ultimately they will be responsible for sports science, the academy - but scouting and recruitment is the primary focus. We have virtually nothing on that side of things and for a club of this size we should never be in that position. We have to quite quickly improve that.
“It’s a chunky six-figure investment on this – it won’t be there on day one but it will only take a few months to get it in place. It’s fundamental – the board have signed it off and it will happen.
“In terms of the local assistant, hopefully that will be sooner rather than later. Pedro is conducting the interviews because he’s the guy who has to work with him. It’s really important that he feels he can build a relationship and build a trust with the person coming in so we’re leaving that up to him, and the final decision on who he wants to go with.”