They knocked back multiple bids from Norwich City, Bayer Leverkusen and Brentford for Norwegian international Ajer.
Brentford, however, have come back in and are set to complete a £13.5million swoop this week.
Another major factor for Celtic could be whether or not they can gain entry to the group stages of the Champions League.
They play Midtjylland in their first qualifier tomorrow night.
Ange Postecoglou will make his competitive bow in that game as he tries to rebuild his newly-inherited Celtic squad.
A £4.5million deal to sign for Swedish international defender Carl Starfelt from Rubin Kazan is all but agreed.
The 26-year-old passed a medical in Moscow last week and has also agreed terms on his Celtic contract.