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Sanderson, who had coached Adelaide since 2012, was axed after a review of the club's football operations, it was announced on Wednesday night.
Former Crows captain Goodwin, currently an assistant coach at Essendon, has been touted as a frontrunner to take over.
Thompson, who coached the Bombers this year but will step down next season when James Hird returns to the job after serving an AFL ban, has also been linked with Adelaide.
Adelaide narrowly lost the 2012 preliminary final in Sanderson's first year at the helm, but the Crows have missed the top eight in the past two years.
The 40-year-old initially signed a three-year contract to coach the Crows.
The deal was extended last December, tying him to Adelaide until the end of the 2016 season, meaning he is set to receive a payout rumoured to be in excess of $1 million.
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"Brenton is a quality person and accomplished coach but recent weeks have unearthed a need for change," Crows chairman Rob Chapman said in a statement on Wednesday.
"Both parties have realised they have different perspectives on where we are at as a footy team.
"It is a tough decision but one the club feels pushes us closer to realising our ambitions."
There is speculation that a player revolt contributed to the axing.
Crows players, including forward Taylor Walker, reportedly criticised Sanderson and some of his assistant coaches in post-season interviews.
Sanderson leaves West Lakes with the highest win rate (57 per cent) of any other coach of the club — 39 from 69 games in charge.
Adelaide sacks Sanderson as coach
