The Norwegian has blossomed over the past 12 months as he's become a mainstay of Neil Lennon's defence.
There has been reported interest in the player this summer with Celtic apparently valuing their asset around £15 million.
Even though the player inked a four-year deal last season, Lennon wishes to fend off potential suitors from elsewhere with a new and improved contract.
The Parkhead boss is said to have named Ajer as one of five players that Celtic cannot sell before the end of the transfer window.
The centre-back joined the Ladbrokes Premiership champions in June 2016 from Start for a fee of around £650,000.