Sky Sports are reporting that both former Chelsea coaches have spoken to officials about replacing Roy Hodgson, who left the Hawthorns to take charge of the England national football team.
Ranieri, 60, has managed a host of huge clubs including Roma, Juventus, Valencia and, most recently, Inter.
He left his position at San Siro in March after a run of two victories in 13 matches and Champions League elimination at the last-16 stage.
Wilkins, 55, has been out of management since two short spells with QPR and Fulham in the late 1990s.
The coach has recent experience at Stamford Bridge as assistant manager to Carlo Ancelotti, Guus Hiddink and Luiz Felipe Scolari.
Chris Hughton, who currently manages the Baggies’ local rivals Birmingham City, remains the bookies' favourite for the job.
West Brom are eager to assess all lines of enquiry before deciding on an individual, and are in no rush to make a decision.
Hodgson was in charge for 15 months before being appointed by the FA as the successor to Fabio Capello.