Odemwingie, who scored both goals in Monday's 2-0 home win over Southampton, has resolved his differences with Nigerian coach Stephen Keshi and has set his sights on reigniting his international career.
Midfielder Youssouf Mulumbu is also set to be absent from the Baggies when the competition gets under way in the new year after Congo DR qualified.
But Odemwingie feels the Baggies can cope with the absence of two of their most influential players as they look to build on their fine start to the Premier League campaign.
He said: "It is a different situation now to maybe my first two years here when my goals were very important.
"Now any player can play well, and we have good players who can play for a whole month at Albion and they will do well without me.
"Youssouf is also a very important player for us in the middle but we have good numbers of players.
"We have Yassine El Ghanassy who is still waiting his chance to show something from one of the wings.
"We have (Chris) Brunt, (James) Morrison, (George) Thorne. We have players who can play at this level and Albion took into consideration when recruiting players that a few of us might go (to the African Nations Cup).
"I know it's going to be a bit of a loss, us leaving for a few weeks, but we hope the players there can follow the team's performance."
Final tilt at continental glory?
Odemwingie is relishing the prospect of trying to help his country to African glory and recognises it may be his last stab at winning the tournament.
He said: "Will I play in the African Nations Cup? Yes, yes. There were a few things to clarify with the present manager (Keshi) because he substituted me in his first game very early in the second half.
"I thought that was a message to me so I was ready for any scenario and I showed that openly.
"But, after speaking to him in the last few weeks, he said it was nothing personal and that the team was playing so badly, that if it was in his power he would have changed everyone.
"Unfortunately for me, he started with me. Everything is now settled and he says if I want to play, I'm welcome. It is my country that I love and of course, I'm going to play for them."
Odemwingie added: "I will put the country and the fans before anything if there are any disputes but I'm a very straightforward person.
"If things are not okay, I don't pretend and say things are fine but definitely I'll put our football fans first in any decisions.
"I know I will miss a chunk of Albion's season but it is hard not to go to this African Nations Cup. It could be my last."