However, the South Korean's agent has revealed the asking price for the Osaka midfielder is now £3million – with the player looking for wages of £1.2m per year.
That could be too rich for Celtic, though the 22-year-old's agent, Lee Yueng Joong, has confirmed he has discussed the player with the Hoops.
He said: "Cardiff City has shown assertive attitudes for the transfer of Kim Bo-Kyung. Because the manager really likes Kim Bo-Kyung, the negotiation is progressing satisfactorily.
"I also have contacted and discussed with Celtic, through my sub-contracted agent who is working in Scotland. I already checked Celtic has interest in Kim Bo-Kyung, but I did not receive any official bid from Celtic yet.
"At present, the transfer fee of him is discussing a level of £3m with some clubs.
"The annual salary of him is also on the table, with around £1.2m.
"I'm still awaiting Celtic's official answer or proposal for Kim with the conditions which I am discussing with other clubs.
"I will leave the door open for this transfer."
Neil Lennon has other signing options, including Rosenborg's 19-year-old star Markus Henriksen.
The Norwegian was available for around £2m, but that price is expected to rise with Benfica now joining German, Belgian and French clubs declaring their interest.
Lennon would prefer to get his signings in before the end of their pre-season preparations.
But the Hoops boss is also looking further ahead to secure what he already has and wants the club to open contract negotiations with Anthony Stokes, whose current deal has entered its final year.
Despite his goals return, Stokes has never really established himself as a first-choice starter.
This has encouraged other clubs, some as far away as Russia, to monitor his situation.
Lennon said: "He had a great season last year and there is scope for him to improve.
"He's a goal-scorer and I wouldn't be in too big a hurry to let him go."