The 20-year-old winger is in the final year of his contract and has been the subject of speculation over his future after so far failing to agree a new deal.
But Rangers manager Ally McCoist insists he would not welcome any further offers for the highly-rated youngster.
"The bid from Bolton was not accepted and I don't want Gregg Wylde to go anywhere. He is a good young talent and we feel he has done very well," he told the club's official website.
"We want him to sign on again with us and we want his progress to continue here at this football club.
"I now have the opportunity to say any further bids we receive for Gregg will not be welcomed either."
Rangers have sanctioned the sale of Madjid Bougherra to Qatar side Lekhwiya but McCoist is now keen to focus on adding to his squad.
He added: "We had a situation recently with Madjid Bougherra where he made it clear he wanted to leave the club.
"Those circumstances were different and to a certain degree, things were taken out of our hands there.
"With Madjid now gone, we are focused more on getting players in rather than getting more players out.
"I'm hopeful with Gregg's case that a resolution can be reached and that we can get to a conclusion we are all happy with.
"This is probably as good a time as ever for a young player to be coming through the ranks at Ibrox and that's the situation for Gregg too, so we hope he signs with us again."
Source: AFP
Source: AFP