The 22-year old has attracted interest from Robins boss Derek McInnes but Shiels wants him to remain with Killie.
"Liam is happy to stay with us. I'm sure he'll get plenty of offers but hopefully we can keep him at the club," he told STV.
"In fact we would be keen to tie him to a new deal."
It is believed that Bristol have come forward with an offer of around £200,000 for Kelly's services.