The 48-year old played with Killie in the 1980s before moving to Australia and he is now in the running to return as manager according to chairman Michael Johnston.
"I've had a couple of chats with Lawrie," Johnston told BBC Scotland.
"He was visiting his parents and I gave him the courtesy of speaking to him as he still harbours thoughts of coaching.
"He has a very good record with Central Coast Mariners and is a person who has a broad skill set.
"While he has a lot of positives, there is the aspect that he's not been involved in Scottish football for a while."
After stepping down from the top job at the Mariners after five years in charge, McKinna took up the role as football and commercial operations manager. Current Socceroos assistant Graham Arnold will take over at Bluetongue Stadium following the World Cup.