The South Korean ace has been tracked by the Gunners throughout his involvement at the Olympics over the summer and has earned rave reviews from their chief scout Steve Rowley.
Now, with QPR, Atletico Madrid and Fulham all in the hunt, Arsenal could weigh in with a bid that is almost certain to be accepted by the Parkhead hierarchy.
Boss Neil Lennon has already stated he is in no hurry to offload any star players and he spoke over the weekend about welcoming Ki back into his plans after his London exertions. But if a bid in the region of £7million comes in then it would represent a massive profit on the player who arrived from FC Seoul three years ago for £2m.
It is unlikely any deal will be done prior to Celtic's Champions League play-off with Helsingborgs, but as the big names line-up Ki is almost certain to be on his way before the transfer window closes on August 31.
Meantime, former Rangers midfielder Alejandro Bedoja is desperate to dump the Hoops and make it into the group stage at their expense after he joined the Swedish side last week on a free transfer.
The American international said: "I got a lot of messages from Rangers friends telling me to knock Celtic out of the Champions League.
"I was a sub at the Old Firm game at Parkhead and I can tell the Helsingborgs players about the atmosphere.
"I will be extra ready for the Celtic match. When I was growing up I always watched the Champions League on TV and I am desperate to get there with my new team."
STV, meantime, will screen Celtic's first leg in Sweden live next Tuesday night with a 7.45pm kick-off.
Hoops midfielder Dylan McGeouch underwent successful surgery yesterday on his broken jaw.
He said on Twitter: "Operation went well today . . . glad to have my family around me as it's times like this you need them! Hopefully be back playing soon."
The youngster, who was injured in the friendly against Real Madrid at the weekend, is likely to be out for between four to six weeks.