寝てるよ

is sleeping

→ 寝る
phrase Common #6,509
is sleeping Casual contraction of 寝ているよ. The subject is understood from context, so it can mean “I’m sleeping” or “he/she is sleeping.” よ adds emphasis or informs the listener.
JA: 今、子どもが寝てるよ。
EN: The child is sleeping now.

自分の部屋で寝てるよ

I'm sleeping in my room.

夏にはいつも窓を開けて寝てるよ

I always sleep with the windows open in the summer.

じゃこの時間に寝てるよ

At home, I’m usually asleep by this time.

— 甘い生活 (1960)

赤ちゃんがベビーベッド寝てるよ

The baby is sleeping in the crib.

僕の父さんよくテレビの前で寝てるよ

My dad often falls asleep in front of the TV.

トムってしょっちゅう寝てるよ

Tom is always sleeping.

いまは叔母さん寝てるよ

My aunt is sleeping right now.

— すずめの戸締まり (2022)

トムってもう寝てるよ

Tom’s already asleep, right?

トムならソファ寝てるよ

Tom's sleeping on the sofa.

箱の中猫は寝てるよ

The cat in the box is sleeping.