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.
Wise, 42, is among several big names showing interest after Brendan Rodgers quit for Reading.
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.