The 32-year-old is leaving Brunton Park after 12 years and Shiels is close to a deal.
The Kilmarnock manager, who is also aiming to sign goalkeeper Craig Samson from Saturday's Clydesdale Bank Premier League opponents St Mirren, said: "We have Peter Murphy from Carlisle. I am confident we can cross the line with that one."
He added: "He is an experienced left centre-back who has over 400 games for Carlisle behind him.
"He is a top player. He fits our needs and he has the quality as well."
If he completes his deal, Murphy will be able to help nurture 19-year-old centre-back Lee Ashcroft, who made his debut for Killie in last weekend's 3-2 win over Dundee.
The teenager followed that by signing a new three-year contract and then scored on his first start on Wednesday in the 3-1 defeat by Hibernian.
Ashcroft said: "First of all I was absolutely delighted at getting offered my new contract and to get my first start the other night was absolutely amazing.
"It was the best experience of my life. I was obviously a bit gutted about the result. When I got my goal to make it 1-1 I thought we had a chance to go on and win it.
"To lose the game so late was a bit disappointing but we will learn from the mistakes and hopefully improve on that."
- Sports & Recreation
- Clydesdale Bank Premier League
- Craig Samson
- Lee Ashcroft