Enciso was involved for 45 minutes of a 2-0 win against Anderlecht’s youngsters this week.
Given Enciso has not been playing regularly in the Premier League, he wanted to get match sharpness.
The Albion head coach Fabian Hurzeler said: “I watched him. First of all, I think it's a great thing when a player came by his own to me and ask me if he can play for the under-21s to stay in the rhythm.
“That's a great signal and a great thing that he wants to improve, no matter in which team.
“So now he played for the under-21s, but he's also a very important player for us.
“It's a little bit the same with Evan (Ferguson). They are doing good in training, they are in good shape mentally, physically.
“They both scored for their national team, so they are in great shape. But the others are also in great shape.
“Danny (Welbeck) is in great shape. Joao (Pedro) comes back strong. Georgi (Rutter) is in good shape.
“It's competition. Competition is part of the business, you need to make sure that you're ready when you get the chance, you need to make sure that you try to give everything in training to not let yourself down, to not get yourself in a bad place.
“When there is the opportunity, and I'm sure there will be an opportunity next week because we have a lot of games, make sure that you're ready for this opportunity.”
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