Neil Warnock has ruled himself out of becoming Sheffield Wednesday's manager, claiming the move would be too divisive.
Manchester United midfielder Shinji Kagawa has admitted it should be no problem for him to play on the left.
Laudrup is keen to bolster his attacking options before the close of the transfer window and he is weighing up a move for unsettled Albion man Odemwingie.
Odemwingie is out of favour at The Hawthorns and has been told he does not figure in Steve Clarke's plans after failing to push through a move to Queens Park Rangers in the January transfer window.
The likes of Stoke, Cardiff City and Crystal Palace are all thought to be chasing Odemwingie and Laudrup has confirmed he is an admirer of the Nigerian.
"We want to add one more who can give us that in a certain part of the game or in certain games," Laudrup told the South Wales Evening Post
"And he (Odemwingie) is a player with pace who knows the league."