Ajer is expected to move on from Celtic when the summer transfer window opens and the Norwegian is tipped to have a number of options on his table.
Italian giants AC Milan have been tracking Ajer, while newly promoted Norwich City are keen.
Newcastle are also admirers of the centre-back and, in a boost to their hopes of signing him, it has been claimed that moving to St James’ Park appeals to Ajer.
Celtic are claimed to value Ajer at around the £25m mark, however the Bhoys may have to reduce that figure as he is entering the final year of his contract in Scotland.
The 23-year-old will be free to sign a pre-contractual agreement with another club in January if he does not extend his Celtic contract.
It has been suggested that Newcastle will offer £8m for Ajer, but the jury is out on whether Celtic will accept a proposal so far below their valuation.
If Ajer, who is claimed to feel moving to Newcastle would represent a good next step in his career, pushes for a move to St James’ Park then that could pressure Celtic to deal with the Premier League side.