Laws' departure follows a dismal run of results - including yesterday's 3-0 defeat at Leicester - which has seen the Owls slip into the Championship relegation zone.
Assistant manager Russ Wilcox and development coach John Dungworth have also left their positions at the club, with academy manager Sean McAuley taking over as caretaker boss.
Shearer was also linked with the job at Sheffield United when boss Kevin Blackwell was under pressure following a bad run.
The former Toon skipper said: "I am hoping to be back in the game soon, but it has to be the right job".
Wednesday are a huge club, with a massive fan base, and what could be better for Shearer to start his managerial career?