The 25-year-old spent two months on loan at Rugby Park last season after failing to establish himself at The Valley.
The former Dunfermline ace made five appearances during his short stay at Killie and boss Jim Jefferies wants to make his signing permanent.
"Kilmarnock are hopeful and confident that we will be able to tie up a permanent deal for Greg Shields in a few days," said Jefferies.
"We have spoke to both Charlton and the player. Both clubs are nearly there and the deal is virtually certain to go through.
"There are just a few minor details to be ironed out before it is all signed sealed and delivered."
Meanwhile, Jefferies has dismissed reports linking him with a move for Bradford duo Eoin Jess or Gary Locke.
Jefferies signed both players during his tenure in charge of Bradford and both are on the look-out for new clubs after having their contracts terminated at the cash-strapped Yorkshire club.
"There will be a lot of players available this summer but we have not made a move for anyone," said Jefferies.
"It is almost inevitable that Kilmarnock are going to be linked with players like Gary Locke and Eoin Jess because I took them down to Bradford City with me when I was manager.
"Kilmarnock are like every other club and we are working to a budget and we are looking at a lot of options before we definitely decide to make moves to strengthen our squad."
