Sunderland are already in contact with managerial candidates.
Roberto Di Matteo and Gus Poyet are both being linked with the post.
The Daily Mail says initial contact has already been made with Di Matteo and Poyet's representatives, given they are both out of work.
Poyet is looking to get back into football management after his bitter departure from Brighton in summer and would jump at the chance to take over from Di Canio.
However, Di Matteo is likely to need some persuading if he is to follow in his countryman's footsteps by taking over at the Stadium of Light. It is understood the former Chelsea manager, who won the Champions League at Stamford Bridge, wants a more high-profile club as he plots a return to football.