The Baggies are expected to move for Carew if, and when, Darren Bent completes his club-record move from Sunderland to Villa.
Ready for the challenge: Odemwingie insists he would welcome the signing of Carew
Baggies boss Roberto Di Matteo has already confirmed Carew was a player on his radar, but Odemwingie, who has netted seven goals this season, will thrive on the competition.
Eyeing a move: Carew is set to join the Baggies
The Nigerian international said: 'Will I welcome a new striker? You cannot avoid this. 'Every team has competition between players. It's something that must be there and we have it now.
'I'm not the only player who can play and score but just at the moment they (the club) feel I'm in a better condition and I'm confident in front of goal.
'Tomorrow it might be someone else because we have 40-odd games a season.
'If someone else comes in and he's good then maybe you will need to do extra that you've never done before to get a shirt. I know that.'
Former CSKA Moscow striker Odemwingie has had a hectic schedule since the beginning of March with the season in Russia, the World Cup and after joining Albion.
He has picked up a series of niggling injuries, including ankle and knee problems, but feels he is now close to full fitness again.
He said: 'Myself now physically I am getting close to being 100%. "I hope that will be all for me injury wise for this season.'
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