The Robins sit just one point above bottom placed Barnsley in the Championship, and have reportedly offered £200,000 for the Scot, who is believed to be keen to return to England.
Kelly's contract expires at the end of the season, and while the former MK Dons player has not rejected the offer of a new contract, Shiels is hopeful he will stay.
Speaking to STV, Shiels said: "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.
"In fact we would be keen to tie him to a new deal."