Former England defender Stuart Pearce is the latest name to be linked with the vacant Albion manager's job.
Ex-Wimbledon boss Terry Burton and former Portsmouth manager Graham Rix have already expressed an interest following Peter Taylor's resignation on Monday.
Alan Cork, the former Albion assistant manager, is also thought to be in the running.
Taylor recommended that assistant Bob Booker should be his replacement, while Hinshelwood may also be in the frame.
Albion's official online bookmaker BHA Bet have installed Burton as the favourite at 9-4, followed by Cheltenham manager Steve Cotterill at 7-2. Booker, former Seagull Danny Wilson, currently Bristol City boss, and Cork are at 4-1.
Read why Peter Taylor quit Albion plus all the reaction at thisisthealbion.co.uk
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