Smith, popular with Wednesday fans for his no-nonsense approach in the 80s, has been part of the youth and reserve-team set-up for two seasons at Hillsborough.
The Owls have stated that they are not giving up on their academy though - as Sean McAuley will continue to oversee it.
Smith took charge when Wednesday faced Coventry City in the league cup two season ago as caretaker manager before Paul Sturrock was appointed.
Sturrock is confident that Smith will find work in a similar role with another club in the next few weeks.
Meanwhile Arsenal's Mart Poom and Manchester City's Nicky Weaver are the latest goalkeepers to be linked with a switch to Hillsborough.
Poom has had difficulty establishing himself in north London following a move from Sunderland while Weaver, on loan at S6 last season, has just signed a new deal at Eastlands.