The burly striker has missed the majority of the last two seasons with a series of injuries, but he has recently returned to Premier League action for the Hammers.
He netted his first goal since his comeback at Stoke over the weekend, with a trademark header from a set-piece.
Although his style of play is slightly unfashionable in the modern era, Allardyce believes that the battering-ram of a forward would be a useful tool for the Three Lions boss to have in his armoury for the showpiece tournament in Brazil:
“Headed goals can never go out of the game,” he is quoted by the Daily Star.
“Anybody that tries to take headed goals out of the game destroys the game as an entertainment, and diminishes the entertainment value.
“Andy is one of the best headers of the ball you will find and he showed that against Stoke.
“Not only did he head the ball in the net, he had some of the biggest defenders in the game against him and they couldn’t cope.
“Ryan Shawcross fouled him six times and that’s how much trouble he was causing a player of that ability.”
Carroll’s goal saw him tower above both Ryan Shawcross and goalkeeper Asmir Begovic to nod the ball into the Stoke net.
The burly front-man starred for England at EURO 2012 under the guidance of Hodgson, but his fitness worries and the form of players such as Daniel Sturridge, Jay Rodriguez and Rickie Lambert may see him fail to make the cut.