It is not known what the Latics offered for the 30-year-old Nigerian international.
"Peter enjoyed a fantastic first season with us and is a firm favourite with the supporters, with whom he enjoys a great relationship," said technical director Dan Ashworth.
"We have no intention of selling Peter and we are a little bit disappointed that Wigan have tabled this offer.
"We spoke to Wigan beforehand and made it clear Peter was not for sale, but they still proceeded to lodge a bid - which has been flatly rejected," he added.
Odemwingie, who moved to the Hawthornes in 2010 from Lokomotiv Moscow for an undisclosed fee, ended last season as the Baggies' top scorer with 15 league goals.