The 22-year-old winger has also caught the attention of Championship side Cardiff. Lennon revealed after Celtic's 0-0 pre-season draw against Augsburg he had seen the Cerezo Osaka star in action but that no deal was in place.
"He's a player we've been linked with, but there's nothing more on that just now," he told the Daily Express.
"I don't know him personally but I've seen him play. He's a creative type but there is nothing more in it just now. There will be a lot of players we're linked with but we've narrowed it down to a few."
Kim, who has scored twice in 13 international appearances, has targeted a move away from Asia as he looks to progress his fledgling career.
"I want to play in the UK or Germany and Celtic and Cardiff City would allow me to develop," he said.
"I have no experience in Europe, so I am happy to learn step by step."
James Forrest captained the side in their friendly draw in Germany, while Beram Kayal also started after recovering from an ankle injury that ruled him out of the second half of last season.
- Sports & Recreation