The 22-year-old midfielder has been on fine form for the Ayrshire side and bagged a double in last week's win over Aberdeen.
Kelly is out of contract at the end of the season, but Shiels hopes he will be persuaded to pen a new deal.
He said: "I think he's got some time to serve here and it's important that he stays where he's learning.
"We want him to stay in an environment that's good for his improvement and the SPL is certainly providing him with that.
"We are a development club, we are developing players. Liam was let go by MK Dons and we picked him up.
"We've developed him to this level now and we're doing it with other players. I think he's due to sign a good contract."
Kelly is suspended for Sunday's visit of Hibernian and Shiels added: "It's a big blow. He's a player who has been doing really well.
"But it gives someone else the chance to step in and put in a good performance."