West Brom dismissed Pulis less than 48 hours after their humiliating 4-0 defeat to Chelsea, which left the Midlands club hovering just one point above the relegation zone.
And Allardyce, who left Palace in the summer stating his desire to step away from football management, is in the frame to take the hot seat at The Hawthorns.
Former Northern Ireland manager Michael O'Neill heads a list also including Nigel Pearson and another ex-Eagles boss Alan Pardew.
West Brom recorded just two wins in their last 21 Premier League games under Pulis in a rotten sequence stretching back to last season.
Pulis, who was in charge for nearly three years at West Brom, has never been relegated in 25 years as a manager.
Pulis becomes the fifth Premier League manager sacked this season following the dismissals of Frank de Boer (Crystal Palace), Craig Shakespeare (Leicester), Ronald Koeman (Everton) and Slaven Bilic (West Ham).
The Baggies travel to Wembley on Saturday to take on Tottenham, who sit fourth in the Premier League table with 23 points and Greg Megson, boss of West Brom between 2000 and 2004, will take temporary charge.
Michael O' Neill 5/2
Sam Allardyce 11/2
Chris Wilder 14/1
Alan Pardew 8/1
Derek McInnes 7/1
Nigel Pearson 10/1