The Manchester Evening News says Moyes wants to make a swift return to management.
The former United boss is understood to be eager to restore his reputation after his disastrous 10 months at Old Trafford.
A close source revealed: "He feels like he's got unfinished business. If you thought he was ambitious before, watch him now."
Moyes has already been linked with Newcastle, Aston Villa and Tottenham since being sacked by United.