The Swans manager confirms that he wants competition for the likes of Wilfried Bony up front and the wantaway West Brom striker fits the bill with his pace and experience.
Laudrup is keen to provide competition for offseason signing Wilfried Bony up front after releasing Luke Moore and telling Leroy Lita that 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 told reporters. "And [Odemwingie] is a player with pace who knows the league."
The Nigerian has been frozen out of the first-team picture at the Hawthorns after attempting to force through a move to QPR in the January transfer window and repeatedly criticizing the club on Twitter.
Odemwingie joined West Brom from Russian Premier League outfit Lokomotiv Moscow in August 2010.