Wanderers had reportedly made an offer of around £400,000 for the 20-year-old winger but Rangers manager Ally McCoist has turned down that bid and has revealed that he would not welcome any more.
"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," McCoist 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."
Wylde has entered the final year of his Gers contract and has so far failed to agree an extension.