Ajer is keen on ending his five-year stint at Celtic this summer and he has admirers in the Premier League, with Newcastle United and Norwich City keen on acquiring his services.
A £6m fee has been mooted with Newcastle claimed to be frontrunners in the chase to take Ajer south of the border when the transfer window swings open.
Hangeland is of the view that the Hoops defender has all the prerequisites to become a world class player but for that he needs to be at a club where all aspects of his game are tested week in and week out.
The 39-year-old backed Ajer to make substantial improvements in his game if he finds the right club, where he will be pushed to his limits both physically and mentally.
“I think it is important for Kristoffer to reach a higher level now”, Hangeland told Norwegian daily Verdens Gang.
“He is a [defender] who has all the prerequisites to be extremely good.
“To become that, he must more often have the whole spectrum tested, both physical, tactical abilities and in important matches.
“He needs to feel that he is being tested to the max every single weekend
“If he finds a club where that happens, he will experience an enormous development.”
Ajer has won three Scottish Premiership titles with Celtic during his stint in Glasgow and it remains tor be seen where he ends up next as he looks to take the next step in his career.