Rather than send them out on loan, which had been established policy under Sir Alex Ferguson, Moyes is considering whether to keep them at Old Trafford to allow them to continue their development.
"Both have done well," said Moyes. "They have adapted well and made contributions to the team.
"It's a tradition at United to try and get young players into the team and both have come through the system.
"Hopefully we can get both some playing time next season but both need to keep their levels up and keep making an impact in training and games."