The 20-year-old is set to start a game for the Hammers since joining in January 2012, but scored six times during pre-season and was afforded a cameo against Newcastle on Saturday
The 20-year-old moved to Upton Park from Manchester United in January 2012, but made just one appearance before being sent to Birmingham City on loan for the 2012-13 campaign.
Morrison impressed during his time with the Midlands side, scoring three goals in 27 league appearances, and has already shown signs he is also ready to do so at West Ham after netting six times during pre-season.
And ahead of his side's first Capital One Cup fixture of the season, he hopes to be rewarded with a first start, telling the club's official website: "It was good to be on the pitch and I really enjoyed it.
"I thought we played well and defended solidly and I'm glad we got a point away from home as well.
"I feel good that the manager had the confidence to send me on for the final 15 minutes of the game when it was still in the balance.
"I feel I can contribute to the team going forward and defensively. I hope I can do so again when I'm given another chance."