Asoro has been training with Sunderland’s first-team squad in the build up to the campaign.
The 17-year-old even bagged his first goal for the senior side in Sunderland’s friendly against Dijon.
And Moyes said: “The young centre-forward – Joel – played really well. Based on his performances, he will be training with the first-team squad because he deserves that.
“Sometimes you can blow these kids up too quickly and that does happen, but he is one that you have to say is close and there are one or two others who have done well.”
Sunderland have a lack of striking options, so Asoro’s emergence serves as a boost going into the campaign.
Jermain Defoe is currently racing against the clock to ensure that he is fit for the start of the new campaign.
Defoe is suffering with a thigh problem, and Fabio Borini will be forced to play up-front for Sunderland if the veteran hitman does not make it back in time.
Sunderland will also be keen to sign a new forward before the close of the transfer window.
Sunderland start their campaign with a match against Manchester City at the Etihad Stadium.