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."
Meanwhile, Shiels claims he has no regrets over comments made regarding match officials.
The Killie boss, who is serving a three-match touchline ban, faces another Scottish Football Association hearing for accusing Andrew Dallas of "fabricating" evidence.
Shiels hit out after escaping further punishment for being sent to the stand in a Rugby Park match against St Johnstone last month, when Dallas was fourth official.
The Scottish Senior Football Referees' Association welcomed the decision by SFA compliance officer Vincent Lunny to issue a notice of complaint for what they described as an "unprecedented attack" on the integrity of an official.
But, speaking on Friday, Shiels said: "I've got a clear conscience.
"No matter what people say about you, if you've got a clear conscience, no-one can hurt you. You can fear nothing.
"That's where I'm at, I'm in that place. Not everyone can say that.
"When you're sinned against, like I've been, you don't regret anything.
"No-one has shown remorse to me and I'm surprised at that. But it's important that we put it behind us and move on."