Skelton is expected to leave stricken Gretna following their move into administration and a number of clubs are tracking the 27-year-old.
Killie boss Jim Jefferies is a big admirer of Skelton and is hoping to lure him to the club.
"I've had a chat with Gavin but he'll probably have three or four clubs after him," Jefferies told the Daily Record.
"He is 27 now and has SPL experience. I feel he is a player who can play in two or three positions and that is vital to us."