The 17-year-old striker joined from Yeovil Town earlier this year in a swap deal that was due to take 20-year-old Andre Wright to Huish Park on loan.
Although Wright's loan deal fell through because he had already played for two clubs this season, Morton remained at the Baggies and has been training with the first team.
“We've brought the lad in from Yeovil who has trained with us," confirmed Pulis. “He's done really well and we've been pleased with him.
"But we don't want to get into a situation where we're having hundreds in and then there's no time to view them. We want to see them in small groups."