Bluebirds boss Malky Mackay is keen to bolster his attacking options ahead of the new Premier League campaign - but has been frustrated in his attempts to land Blackpool boss Tom Ince, who is believed to have turned down a move to Wales despite his club agreeing a fee for his services.
The Birmingham Mail reports that Albion outcast Odemwingie is now on Cardiff's radar, but he has a number of summer suitors, with Crystal Palace, West Ham, Swansea, Hull and Fulham also reportedly interested.
Palace were believed to be at the front of the queue for his signature and have held discussions with Albion - but the two parties are still some way apart in their valuations of the 32-year-old.
Odemwingie is almost certain to be left out of Albion's eight-day trip to Austria, having not been included in first-team duties since the players returned to pre-season training earlier this month.
He still has a year left to run on his contract at West Brom, but reports suggest that a bid of around £1.5million could be enough to lure the Baggies to the negotiating table.