The precocious 20-year-old played for the last 15 minutes of Saturday's goalless Barclays Premier League draw at Newcastle after earning rave reviews for his pre-season performances.
Now Allardyce is ready to give Morrison his chance as he prepares to make a number of changes for the Upton Park fixture, also including giving a full Hammers debut for new signing Razvan Rat.
Allardyce said: "Ravel is an emerging talent and we've very pleased with what he did in pre-season for us.
"He is an exceptional talent who we hope we can nurture into the fray. Some people might say sticking a player on at that late stage might be risky but we've got to do it at some stage."
Allardyce signed Morrison from Manchester United in January 2012 but sent him out on loan to Birmingham for the duration of last season, where he scored three goals in the Blues' Championship campaign.
Allardyce added: "We can see the talent and the only way to do it is to get him in the first team and get some minutes on the board.
"He'll play against Cheltenham and we'll see how he does and keep an eye on him.
"He's had a good season at Birmingham and he's brought that back with him in pre-season and it's great to see that talent is emerging."
New signing Stewart Downing could keep his place in the Hammers line-up after admitting being short of match practice since his summer move from Liverpool.
Downing, who has played in League Cup finals for each of his previous three clubs, told the Hammers' official website: "For me personally I just want to keep playing and get a good run at it.
"A lot of teams disregard the League Cup a little but I always think if you go strong in it, you've got every chance."