Morrison has made 10 Premier League appearances for the club this season, scoring three times, but is yet to make a senior appearance for the national team.
However, with the 20-year-old having done his England chances no harm with his form this season, Allardyce wants him to continue improving and challenge for a spot in Roy Hodgson's squad for Brazil 2014.
"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. He's going to have to continue his improvement to have any chance," he said.
"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."
Fellow midfielder Jack Wilshere stated recently that he does not consider himself a guaranteed pick for the World Cup, labeling Morrison as a potential rival.
However, Allardyce backed Wilshere to retain a spot in Roy Hodgson's line-up, provided he plays regularly for Arsenal.
"Jack Wilshere's got that final pass, that little bit of creativity," he added.
"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."
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