He is asleep/sleeping.

[Tan Elaine]

Which word should I use in the following sentence?

He is asleep/sleeping.

I remember reading that I should use 'asleep'.

Thanks.

[SoothingDave]

Either is fine.

[Modest Man]

As SoothingDave mentioned, both are Ok.
Just want to add another point.
'Sleep' is a verb, while 'asleep' is an adjective. When you say "He is sleeping.", you're using present continuous tense.