The controversial Nigerian has been expected to leave The Hawthorns all summer, after a very public falling out with the club in January.
Odemwingie attempted to force through a move to QPR at the start of the year, but was told on no uncertain terms that he was to remain a Baggies player.
Cardiff were believed to be interested in his signature at the start of the current transfer window, however their pursuit of other targets saw their interest cool.
Now, the Bluebirds are back in for the 32-year-old, after his proposed move to the Middle East to join Al Nasr collapsed.
Mackay is hopeful that the versatile attacker can add some Premier League know-how to his squad as they embark on a season in the top flight.
West Brom are keen to offload the troublesome forward, as they attempt to free up space, and funds, for a loan move for Manchester City winger Scott Sinclair.
Cardiff are also keen on Ecuadorian ace Jefferson Montero, who is believed to be rated at around £3m by Mexican club Morelia.
Does Peter Odemwingie deserve another crack at the Premier League?
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