Manager Stale Solbakken and newly-appointed coach Brede Hangeland have each said the defender isn’t challenged enough by forwards in the Scottish Premiership and should be looking to move up a level this summer.
Ajer is expected to leave Parkhead in the next window with only 12 months remaining on his deal and Celtic likely open to selling so they don’t lose the 22-year-old for nothing.
This would be thoroughly welcomed by the Norwegian coaching staff who see Ajer as a player capable of shining in one of Europe’s top five leagues.
Solbakken told Norwegian newspaper VG: "He has to change league now. He must. He does not have enough challenges in everyday life there.
"He should go to one of the five major leagues. He has the prerequisites to play in all those leagues. I'm calm about that."
Former Fulham centre-back Hangeland says he’s spoken personally to the centre-back about his future.
He added: "I've told him on the phone a couple of times. In some matches he plays in Scotland, he looks like a senior who plays at junior level.
"It's of course because he's good, and this is not criticism of the Scottish league, but he needs to be challenged more on making choices, on speed, on physics, on everything.
"If I were him, I would try to get to a higher level."