The 22-year-old centre-half has been a key part of Celtic’s success over the last couple of campaigns and his performances have turned heads in Europe.
AC Milan are stated to be interested in taking him to Italy and the Norwegian has also been mentioned with a move to England, with Liverpool believed to be tracking the player.
The Reds sold Lovren to Zenit St Petersburg for a sum of £10.9 million, and are yet to bring in a centre-back to replace the Croatian.
Although the Reds have dipped their toes in the transfer window to sign Kostas Tsimikas, they might need to rope in another centre-half.
A report by Liverpool Echo claims that Ajer is attracting the Premier League giants’ interest.
The club like keeping the ball and their style of play would suit Kristoffer. He could turn into a top centre-half, as he is still young and has shown a lot of potential.
A backup role would be fine for the player, so he can slowly be integrated into the starting XI and become a first-choice defender in the longer run.
A move to the Hawthorns is also understood to be a possibility and West Brom are interested in exploring the possibility of landing the Celtic centre-back.
He is being considered as an alternative target to Brighton’s Shane Duffy at West Brom, but there are obstacles towards sealing a deal.
Celtic are under no pressure to sell the centre-half and are expected to demand an eight-figure transfer sum from interested clubs including Jurgen Klopp’s side, for Ajer.