The defender will be in South Africa for at least two weeks at the end of January and into February.
It is one if the reasons the Hoops gaffer is assessing what he needs when the transfer window opens in just over a fortnight.
Lennon wants to add another defender and a wide left player with pace.
Celtic face Hearts on January 19 before heading to Hamdpen to take on St Mirren in the cup semi-final eight days later. They then play Kilmarnock on January 30 before their William Hill Scottish Cup tie against Raith Rovers on February 2 before a trip to Inverness a week later.
Depending on how far Nigeria progress, Ambrose could out of all those games.
Lennon said: "Efe will be going to the African Cup of Nations. He has been playing very, very well and is an excellent player.
"I hope he enjoys playing for his country and comes back injury free.
"We have got a squad to cope with the time he will be away."
Lennon could have a few more faces in the squad by the time Ambrose heads off to the finals.
American wonder kid Juan Agudelo could be one of them, though another recent trialist, the Ghanaian winger Frank Acheampong, will not be the subject of a bid from the Hoops.
The in-demand Agudelo has headed off for a break as the 19 year-old's MLS season with Chivas USA has just ended, and Lennon said: "He has gone home and we have been in negotiations.
"I don't know where we are with that as I have had a lot on my plate."
Lennon added: "He is someone we like. Whether we can do something there, we don't know.
"He's having a bit of a break because the American season has just finished.
"We would look to pursue him again, but Frank Acheampong is one we will not be pursing."
Gary Hooper's agent is another man Lennon would like to speak to as he believes negotiations to get the strikers' name on a new contract are edging closer to being finalised.
But there is no movement with Victor Wanyama. The Kenyan could be the subject of a substantial offer from Manchester United, Arsenal or Everton when the window opens.
But unless it is a massive bid Celtic will refuse to consider it.
Both stars are set to face St Mirren tomorrow, and Adam Matthews should have recovered from the tight groin which forced him off at Arbroath.
But Joe Ledley is still being rested, and Kris Commons has suffered a complication in his recovery from the thigh injury he received against Spartak and will be out for at least another week.