The Sun says Pardew is lining up Odemwingie as Demba Ba's replacement.
Ba plays for Newcastle tonight for the first time since trying to seal his dream move to Chelsea.
Talks were on-going last night and Toon boss Pardew is hoping to land Odemwingie for £3million.
The Nigerian, 31, has 18 months left on his deal and wants to quit Albion.
He almost moved to the cash-rich Qatari League last summer but the Baggies were unable to strike a deal.
Albion chiefs are keen to do business now rather than see his value plummet as he nears the end of his contract.