The Hoops have already rejected an offer, reported to be about £5million, from Norwich, but manager Neil Lennon bracing himself for the Canaries to make another bid before the transfer window closes.
And Ledley, who is hoping to have finally shrugged off a pelvis problem which had been troubling him recently, said: "Gary is one of our main players, he links up play and scores goals so hopefully we can keep him. Everyone will want to sign him because of what he has done but hopefully he is happy and will stay here for a long time."
He went on: "I wouldn't be surprised if more bids came in, he is a talent and a goalscorer and he showed that yesterday.
"But the players, management and fans want him to stay.
"He has a year and a half left (on his contract) which is a long time so hopefully he can continue his form and the speculation goes out the window."
The Wales international revealed he has the same problem which bedevilled captain Scott Brown for the first half of the season.
He said: "It is my pelvis, similar to Brownie.
"It depends how I feel. Sometimes when I wake up it is okay, the next day it can be hurting. So I just take it day by day.
"We had exactly the same injection and Brownie is flying now so hopefully it can continue with me."