Jack Wilshere has expressed concern for his place in Roy Hodgson's squad for Brazil due to the development of the likes of Morrison, who is reviving his career at Upton Park after leaving Manchester United.
The 20-year-old has represented England at four age groups but has yet to be included in the senior squad.
"At the moment he's got to keep showing improvement with us and it's a long way between now and the World Cup squad being picked," said Allardyce. "He's going to have to continue his improvement to have any chance.
"It should be a dream of his, and can he make that dream a reality?
"It's an ultimate goal he's trying to reach. If you are dedicated enough in your time on and off the field, then you can get there."
Wilshere's progress has been delayed by long-term injury, but Allardyce has no doubt over the Arsenal midfielder's talent.
"Jack Wilshere's got that final pass, that little bit of creativity," Allardyce said.
"With the amount of competition Arsenal have in that position, it's going to be more of a concern for Jack to play in Arsenal's team, for me, on a regular basis, than thinking about the World Cup for England.
"If he does both he'll be there."
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