The 20-year-old, who joined the Hammers from Manchester United in 2012, spent the second part of last season on loan at Birmingham City.
"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 told Press Association Sport.
"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."
Morrison has featured from the bench in the Premier League this season.