The 20-year-old, who is in the final year of his current deal at Ibrox, will be free to sign a pre-contract agreement with another club in January.
Wylde has been the subject of increasing speculation over his future after he failed to agree new terms with the Light Blues following recent talks.
Rangers are adamant they want to retain his services and are unwilling to allow the player to leave for the sum on offer.
Rangers manager Ally McCoist insists he would not welcome any further offers for the highly-rated youngster.
He told the club's official website: "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.
"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, rather than see it depleted further.
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: Team Talk
Source: Team Talk