The Baggies have looked short in midfield after lacklustre performances against both Manchester City and Watford in the Premier League. And the controversial free agent is now as low as 5/1 to join West Brom to help solve their problems in the middle of the park.
Championship side Derby County remain favourites, however, with both the 32-year-old's former club Newcastle United and Scottish Premiership champions Celtic currently ranked as having an outside chance by Sky Bet.
Derby are 11/8 to sign Barton, while Newcastle are priced at 8/1 and Celtic 14/1.
Interestingly, West Ham are still second favourites despite announcing they will not sign the midfielder, with Nottingham Forest shortly behind them.
Where is a good fit?
But West Brom's stuttering start and need to strengthen could well be a recipe for the 32-year-old's arrival at the Hawthorns. Most have passed up on the opportunity on the controversial character but Tony Pulis has never been afraid of a challenge.