Wilkinson, who has hosted Today alongside Gold Logie winner Karl Stefanovic for the past four years, is believed to have expressed interest in taking a new television role, according to The Daily Telegraph.
Rumours of Kennerley quitting her show first surfaced when she took some time off last month and was temporarily replaced by Getaway star Catriona Rowntree. Rowntree later said that she was not sure how she could "make it work" being on a morning show full-time with two young sons at home.
Stefanovic is also believed to be leaving Today for a full-time role on current affairs show 60 Minutes. Radio star Ben Fordham is rumoured to be after his old job, while Georgie Gardner has been named as Wilkinson's most likely successor.
Kennerley recently said: "These days you are either wanted or you are not. You perform or you don't. They want you or they don't. It is not actually all that complicated.
"I have had a thoroughly fabulous time, I have enjoyed it. It has been nine years. We have done very well. Everything has to regroup so I am looking forward to it. If you don't like change, don't be in TV."
When asked about the Wilkinson rumours yesterday, a television insider joked; "Yes, and Elvis Presley is doing the weather."
Rival Seven Network bosses recently denied rumours that Melissa Doyle is quitting Sunrise to join Today Tonight.
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