Following a string of impressive displays in the Premier League and for England's Under-21 side, the Hammers boss is keen to keep his star youngster's feet on the ground
Morrison has earned rave reviews after scoring four goals for the London club and also catching the eye for England Under-21s, notching another two goals in a victory against Lithuania this week.
But Allardyce joined England manager Roy Hodgson in playing down the midfielder's chances of being on the plane to Brazil.
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"At the moment he's just started with the under-21s, and of course he's played very well in those games, but there was little or no competition there so I'd have expected that.
"I have to be careful with the amount of publicity that Rav gets to make sure that we just continue his growth slowly and continue him playing to the level that he's playing at and try and make him better.
"We've got to make sure there's no distractions that might put a young man off at this stage of his career which can happen. They can have their ups and downs, they can burst onto the scene, they can get lavished with praise and then lose their focus and when they lose their focus they can dip away again and we don't want that.
"Like I said he's in our team and he's enjoying his football with the rest of the lads. He's got to concentrate on the next game and whatever happens at the end of the season will happen."
Allardyce also spared a thought for Andy Carroll, who will be hoping to make the Three Lions squad for Brazil when he recovers from a heel injury.
The West Ham boss added: "I think that the Andy Carrolls of this world will want to get fit and play well for West Ham as soon as he can. It will be at the back of his mind that the World Cup is coming and he wants to be a part of that squad."