None sound correct to me. Sounds like you’re trying to describe a specific situation.

Do any of these help:

• “I’m wondering if the monkey can see my ears”
• ”I’m wondering if that monkey can see my ears”
• ”I’ve been wondering about that monkey and whether it can see my ears”

Is this a fragment of a sentence? Because it seems like an incomplete thought.

If there’s further information to come in the sentence with the monkey as the subject you could use brackets to indicate your thought and write…

“The monkey (about whom I’m wondering: ‘can they see my ears?’) did something or other…”

This isn’t strictly grammatically correct, but seems to be the most natural way it could be written and said without sounding weird.

Or is ‘monkey’ an answer to some other question and you’re adding that other information for context? If so, you could use a semi-colon.

“What’s bothering you?”

“The monkey; I’m wondering ‘can they see my ears?’”

None of them are grammatically correct because none of them are complete thoughts let alone sentences.

All three try to specify the particular monkey by enumerating that it can see your ears but do no more.

Take away the description of the monkeys ability to see your ears and what you’re left with is “the monkey”.

“The monkey” isn’t a sentence.

If you are the subject and what’s happening is that you’re wondering if the monkey can see your ears then the sentence you want is “I’m wondering if the monkey can see my ears.”

If, as I suspect, you’re using “the monkey whose ability to see my ears I’m wondering about” as the subject of some larger more complex and cool sentence then you gotta lay out that part before someone can give solid grammatical advice.

I’m wondering if the monkey can see my ears.

They do all sound stupid.

As it’s a complete statement just say “I’m wondering if the monkey can see my ears.”

Because it is ‘the’ monkey, rather than ‘a’ monkey, it is implied that the monkey has already been referred to.