Trinidad and Tobago forward Jones, 29, is in his second spell at Stoke, having scored three goals in 13 matches while on loan from Southampton in 2005.
He joined on a permanent basis in 2010, netting 13 times in 88 league matches.
Nigeria international Odemwingie only joined Cardiff this season, having fallen out of favour at West Bromwich Albion following a failed attempt to sign for Queens Park Rangers at the end of the 2013 January transfer window.
The 32-year-old has scored once in 15 league appearances since moving to Wales.
"There is potential to do a deal with Peter Odemwingie going to Stoke and Kenwyne Jones coming to us," Cardiff manager Ole Gunnar Solskjaer told the BBC after the 1-0 FA Cup fourth round win over second tier Bolton Wanderers on Saturday.
"I can't confirm anything until deals are done and medicals are done but we are a long way down that road."
(Reporting by Josh Reich; editing by Tony Jimenez)
