YOU SAID:

my cat is on my desk sleeping

INTO JAPANESE

私猫が眠っている私の机の上

BACK INTO ENGLISH

Me on the desk of my cat is sleeping.

INTO JAPANESE

私の猫の机に私が寝ています。

BACK INTO ENGLISH

I sleep on the desk of my cat.

INTO JAPANESE

私は私の猫の机の上に眠る。

BACK INTO ENGLISH

I sleep on the desk of my cat.