The former Newcastle United boss has endured a mixed time of it in east London, returning West Ham to the top flight before receiving regular criticism from some fans over his style of play.
With the 60-year-old out of contract in the close-season, question marks remain over his long-term future at the club, but Hurst believes Allardyce remains the right man for job.
"I think Sam should stay and I am surprised there are people who think otherwise. You should be careful what you wish for," he told Goal.
"I don't see anyone out there who could come in and guarantee doing a better job than Sam.
"There have been some terrific performances this season and the team is moving in the right direction."
West Ham sit ninth in the Premier League thanks largely to an impressive first half of the season, with victories over Manchester City and Liverpool among the highlights of their campaign.
Allardyce's side have also taken points off Manchester United and fierce rivals Tottenham, and Hurst has urged the club's board to stick with their manager.
"What’s been impressive for me has been the level of performances against the top sides," he added.
"The players have really held their own and gone toe-to-toe with them, especially at Upton Park.
"I don’t know what the owners' plans are because obviously the move to the Olympic Stadium is big in their thoughts and they are looking to the future, but I would like to see Sam in charge next season."
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