You can sometimes refer to small children as a 'cheeky monkey'. It's a sort of cute nickname. I'm not certain, but that may just be a British usage. 'Monkey' is also a horrible racial slur towards black people. I am curious as to where you saw a person described as a monkey.

Monkey when used with children, is a term of endearment, it is a pet name, like honey, sweetie, cutie, etc. If a white person calls a black person a monkey it is a racist and mean spirited remark, which is extremely nasty and hurtful

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