The Potters have announced that the deal is subject to both strikers passing medicals and agreeing personal terms.
However, Stoke hope to conclude their move for Odemwingie over the weekend.
Nigeria international Odemwingie only joined Cardiff in September, moving from West Brom for a fee believed to be in excess of B£2million.
The 32-year-old signed a two-year contract and netted twice in his first four games for the Bluebirds - however, he has failed to add to that tally in 13 appearances since.
Jones, a Trinidad and Tobago international once of Southampton and Sunderland, has fared better.
The 29-year-old has netted five goals in 10 games. However, none of them have come in the Barclays Premier League, with four in the Capital One Cup and the other in the FA Cup defeat of Leicester earlier this month.