Allardyce left his role as manager of Crystal Palace after just five months in charge, despite leading the club to Premier League survival.
There's plenty of familiar names on the list of potential candidates to replace the 62-year-old, so here's a look at some of the leading candidates...
The Italian led Leicester to a shock Premier League title in 2015-16, only to be sacked in February 2017 with the club in relegation danger. The 65-year-old has plenty of Premier League experience, having also managed Chelsea, and is thought to be on Watford's wanted list.
If Palace want Hull boss Silva they had better be quick. The 39-year-old Portuguese has reportedly held talks with Porto in his home country and the draw of Champions League football next season may well prove too strong. Silva impressed with the Tigers, despite their relegation to the Sky Bet Championship, and is also thought to be on Watford's short-list.
Hodgson has been out of work since resigning as England manager following their abject failure at Euro 2016. Appointing the 69-year-old may not go down too well with supporters, but his experience could at least bring stability to the Selhurst Park club. Hodgson, who has managed Blackburn, Fulham, Liverpool and West Brom in the Premier League, was said to be considering a role at Championship club Norwich in March of this year but nothing has materialised.
Wales manager Coleman was a firm favourite during a four-year spell as a player with the Eagles between 1991 and 1995, making over 150 appearances. His stock as a manager rose when he led his country to Euro 2016 - their first tournament qualification since 1958. Wales topped a group containing England, Russia and Slovakia, with Coleman guiding his side to the semi-finals where they were beaten 2-0 by Portugal. The 46-year-old, who is now presiding over a World Cup qualifying campaign, may fancy another crack at the Premier League, having managed Palace's London rivals Fulham between 2003 and 2007.
The Serbian has been a revelation at Fulham this season, turning the club from relegation candidates into play-off qualifiers. The brand of football played by the Cottagers was the envy of the Sky Bet Championship, with Jokanovic's men the joint-highest scorers with 85 goals. Fulham were beaten by Reading over two legs in the play-off semi-finals to miss out on a Wembley date and the chance to reach the Premier League. Could that tempt the former Watford boss to leave Craven Cottage for a top-flight job at Palace should they make an approach?
Former Man City boss Roberto Mancini is the second favourite in Sky bet's next Crystal Palace manager market at 5/1.
Fresh from leading Celtic to an unbeaten season on their way to the Scottish Premiership title, Brendan Rodgers, who could end his first season at Celtic Park with the treble, is 12/1 for the job, the same price as Ryan Giggs.
Former Middlesbrough manager Aitor Karanka is also 12/1, while Huddersfield's David Wagner and Reading's Jaap Stam, who will contest the Championship play-off final on Monday are 14/1 to be the next Palace boss.
The rest: Sean Dyche (14/1), Gus Hiddink (14/1), Martin O'Neill (16/1), Nigel Pearson (20/1), Alan Pardew (20/1), David Moyes (20/1), Keith Millen (20/1), Alex Neil (20/1), Garry Monk (25/1). Sergei Rebrov (33/1).