That's despite Kelvin Wilson losing his appeal against a two-game ban.
The Hoops face the prospect of being without their first-choice centre-back pairing for the SPL game against Hearts on January 19 and League Cup semi-final against St Mirren the following weekend.
Celtic coach Garry Parker said: "Good luck to him. Hopefully, they get knocked out early so that he comes back."
Wilson must sit out domestic games after an SFA tribunal found him guilty of violent conduct in an incident with Dundee's John Baird at Dens Park on December 26.
And Ambrose is already on his way to join up with the Nigeria squad which will compete in the African Cup of Nations in South Africa.
The Eagles kick off their group games on January 21 with a game against Burkino Faso.
If they go all the way to the final on February 10, Ambrose would not be available again to wear the Hoops until two days before they are due to face Juventus in the first leg of their Champions League last-16 tie.
The 24-year-old has always maintained that, despite being desperate to represent his country at what would be his first prestigious tournament, he would only do so if Celtic gave him the green light.
Now, with Wilson banned, his absence from the Hoops line-up will be even more sorely missed.
Manager Neil Lennon made no attempt to hide his unhappiness at the SFA tribunal's decision to uphold the automatic two-game suspension for the English defender and said: "Unfortunately, there is no right of appeal. We find it disappointing Kelvin has been found guilty of violent conduct, particularly when the other player involved has stated that it was an accidental incident."
However, despite this setback, Lennon has always maintained he does not want to deny Ambrose the opportunity to play in the African Cup of Nations.
And Parkhead coach Parker has confirmed there is no change in that policy. He said: "He will be a miss because he is a decent player who is good at the back for us and is calm on the ball."
As Celtic looked to step up their efforts to bolster their squad, two players not on the Parkhead wishlist are West Brom's Graham Dorrans and Rubin Kazan's Alexei Eremenko.
But Standard Liege's left-sided defender, Rami Gershon, flew into Glasgow last night looking to secure a deal which could make him a contender to fill the breach at the back.
The 24-year-old said: "I am very excited to have the opportunity to play for Celtic. I just hope everything will be done tomorrow and then I can speak more."
Gershon admitted he had not yet discussed the possible move with Celtic midfielder and fellow- Israeli Beram Kayal.
He said: "He is a good friend of mine, but everything was very quick so I didn't find the time to speak to him. But in the past he has told me only good things about Celtic."