The 23-year-old has a contract with the Hoops coming to an end next year and could put an end to his five-year association with the club this summer.
Newcastle have been credited with an interest in Ajer, while newly-promoted Premier League side Norwich City and Bundesliga outfit Bayer Leverkusen are also said to be keen.
There have been suggestions that the Norway international, who has entered the final year of his contract with Celtic, could be available for as little as £6m this summer.
However, while a £6m deal for Ajer appears to be a bargain, Newcastle or any other interested club face the prospect of having to pay a premium beyond the transfer fee for the defender.
It is said that the centre-back’s agent is touting the player around in an attempt to get the best possible deal during the summer transfer window.
If Newcastle decide to pursue a deal for Ajer, they could have to fork out a significant sum in agent fees and wages to secure the player’s services.
It remains to be seen if having to pay a premium beyond the transfer fee will turn the Magpies away from pursuing a deal for the Norwegian.