The 32-year-old fell out of contract at Bolton yesterday but has been offered a deal to play in the SPL next season.
Club skipper, Wheater, who lives in the town, was holding out hope that Wanderers’ ownership issues would be resolved quickly this summer, enabling him to discuss a new deal.
But with just a month now remaining before the start of the new season it is understood his representatives are now talking with Killie, who have also expressed an interest in keeper Jake Turner.
Kilmarnock qualified for the Europa League this season and play in the first qualifying round against Welsh side Conor Quay Nomads on July 11. They are currently in a pre-season training camp in Marbella.
Wheater signed for Bolton in January 2011 from Middlesbrough for £2.3million and – aside from a short spell as a free agent in the summer of 2017 – has been a first-team fixture under four different managers, not to mention a fans’ favourite on the terraces.
He has played 236 games for Bolton in all competitions and scored 16 goals.