Ajer, 22, is a target for AC Milan this summer, but Brendan Rodgers looks set to make the first move.
Rodgers knows Ajer well from his time in charge of Celtic and the Norwegian was part of his title-winning sides.
The towering defender is on the radar of a number of clubs following three impressive seasons at Celtic Park.
Ajer has made 129 appearances for Celtic since joining from IK Start in Norway.
Celtic will not let their defensive rock go cheaply, with reports earlier this month suggesting a €30m (£27m) asking price.