The Norwegian centre-half is set to become a free agent once his contract with Celtic expires this summer.
Clark told the Daily Record: "Kris is an outstanding player and I really feel for the Old Firm because it's tough for them to compete with smaller clubs in bigger leagues.
"They have such a worldwide fan base and when I managed up there it really hit home how big the two clubs are but they can't compete financially with the giants in Europe.
"I just hope they can get to the level where they can be competitive in the Champions League and keep a hold of the likes of Kris Ajer.
"Well, maybe not in Kris's case specifically because he's been linked with Newcastle United in some north east media outlets!
"So with my Newcastle United fans head on I hope that happens! My mates have all been asking me about him since he was mentioned and I told them if it comes off we'll be getting a real top player.
"But I'm not sure we're in the market for a player of his value with the money that would be involved to land a player of his ability.
"I played with Darren Peacock who was similar in terms of size but he was more of an old-school centre half, physical and strong and Kris Ajer is more in the mould of his partners Steve Howey and Philippe Albert who were ball-playing defenders.
"He has turned into an excellent, accomplished centre back for a huge club like Celtic and obviously the Norwegian international team.
"You've got to have a big character to play for Celtic or Rangers. You can't just be a good footballer. You have to be a big personality, especially if you're going to play for them when they're successful."