The Sun says the ex-Chelsea captain is itching to get back into football two months after being axed as director of football at Newcastle.
Gus Poyet, Wise's former Chelsea team-mate, has also applied for the job.
Former Gillingham boss Andy Hessenthaler and Colchester's Paul Lambert have also been linked.
But current first-team coach Malkay Mackay is favourite to take over as finances look set to dictate the appointment. Rodgers was on around £300,000 a year and Mackay will step up for £200,000.