The former Manchester United youngster has made more headlines off the pitch than on it in his fledgling career, but he has let his football do the talking in recent weeks.
His performances for the Hammers earned him a place in the England's U21 side, and he netted twice in the 5-0 victory over Lithuania this week.
But the 20-year-old, who spent the majority of last season on loan at Birmingham after Allardyce signed him from United, also had an argument with Wilfried Zaha over who should take a late penalty.
Allardyce dismissed the coming together with Zaha as "handbags" before suggesting a place in Roy Hodgson's World Cup squad is not beyond the reach of Morrison.
"It's a little early to tell," said Allardyce. "But I think if he continues to be a regular player with our first team then I can't see any reason why he wouldn't get noticed and maybe be pushing that way.
"But, at the moment, he's just started with the Under-21s and, of course, he's played well in those games but they were little or no competition there so I'd have expected that."
But Allardyce is also keen to play down expectations for Morrison as he does not want unwelcome distractions.
"I have to be careful with the amount of publicity that Rav gets," the Hammers boss added.
"To make sure that we just continue his growth slowly and continue him playing in the team to the level he's playing and try to get him better and then there is no distraction that might put a young man off at this stage of his career, which can happen.
"They can have their ups and downs, they burst on to 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 I don't really want that."