Wigley has taken temporary charge but told the Bristol Evening Post that he has no interest in taking on the position full time.
"I won't be applying for the job," he said. "I've no idea what will happen now, but that is all part and parcel of working in football."
However, McInnes has emerged as a front-runner to fill the Ashton Gate hot seat, although no formal approach has yet been made to St Johnstone by City.
Other names featuring prominently in speculation surrounding the post are Mark Robins, who is also being linked with Nottingham Forest, and Dave Jones.