The Dane is keen to provide competition for close-season signing Wilfried Bony up-front after releasing Luke Moore and telling Leroy Lita he is free to find a new club.
And Odemwingie could fit the bill, with the Nigeria international not featuring in Steve Clarke's matchday squad for West Brom's first two Premier League fixtures.
"We want to add one more who can give us that in a certain part of the game or in certain games," Laudrup said.
"And he (Odemwingie) is a player with pace who knows the league."
Odemwingie has been frozen out of the first-team picture at The Hawthorns after angling for a move to QPR in January.
He moved to West Brom from Russian Premier League outfit Lokomotiv Moscow in August 2010.
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