The FC Seoul midfielder has agreed a January transfer to the Hoops, pending a medical.
Under-fire Parkhead manager Tony Mowbray wants the deal to be done as soon as possible and Hoops powerbrokers are working behind the scenes to have the 20-year-old in Scotland as early as this weekend.
Ki pipped a host of top Asian talent to be crowned the continent's best young player on Tuesday night.
And the skilful midfielder admitted picking up the prize was the perfect way to prepare for life in Glasgow.
He said: "I didn't expect the award at all. It came as a complete surprise for me. It's a huge honour though, probably the highlight of my career so far.
"There are so many talented players in Asia so to be named as the Young Player of the Year was special.
"It was a wonderful evening and the perfect present before I come to Scotland."
Ki has already met up with Hoops striker Scott McDonald when Australia faced South Korea earlier this season.
And he said: "I met Scott when Australia were playing us. At that point he knew I was signing so he took the time out to wish me all the best.
"We chatted for a while about the club and what to expect from it. It was really nice of him. I think he's a really good striker and I'm looking forward to playing with him.
"I know all the players at Celtic. I'm not kidding when I say I follow them.
"There's a lot of quality at Celtic so I know it will be hard for me.
"I think that's a good thing though, you want to play with great players around you."