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”

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.

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?'"

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.

“The monkey about whose ability to see my ears I’m wondering”.

Part of the issue is that the thing you’re wondering about needs to be a noun, but the verb “can” doesn’t have an infinitive or gerund form (that is, there’s no purely grammatical way to convert it to a noun, like *“to can” or *“canning”). We generally substitute some form of “to be able to”, but it’s not something our brain does automatically.

Also, there’s an implied pragmatic context that some of the other comments seem to be overlooking:

• The speaker is apparently replying to a question asking them to indicate one monkey out of several possibilities

• The other party is already aware of the speaker’s doubts about a particular monkey's ear-seeing ability

• The reason this doubt is being mentioned now is to identify the monkey, not to express the doubt.

The monkey that (I think) can see my ears

Makes it simpler without the if-clause.

Parentheses are optional, but help with readability imo

The first doesn't make sense to me.

The second does but sounds weird.

The third looks okay to me, but beware I'm not a native speaker so perhaps I think it's grammatically correct but it's not.

By the way, the sentence feels silly out of context as you present it, and doesn't make much sense by itself but I'm hoping you have some context that frames it such as another character asking "Who are you looking for?" and a story that explains why you would even be concerned they can see your ears. Maybe it's an ear-eating monkey that gets triggered when they see ears. Or maybe they can shoot laser beams with their eyes but only aimed at people's ears. I don't know. There's a reason I'm not a writer.

The monkey, who I wonder if it can see my ears.

Disclaimer: I have Cs in English Class... 😉

The phrase "I'm wondering if... can..." needs a noun or pronoun between "if" and "can". As soon as you try to remove that (by moving it out to "The monkey who..."), the phrase stops being grammatical. We'd understand you, but it would require significant effort to parse the sentence. That seems to be what makes this sound strange, no matter what we try to do with it.

I don't know whether other languages can do this, but English can't.

Generally with animals the "it" pronoun fits best, but i think they phrase itself need reworking, i understand that you can't today say but i think it's a difficult way toc phrase it the way toc wrote it.

Maybe "this is the monkey I suspect is seeing my ears"

The monkey, of whom I'm wondering if it can see my ears.

If your wondering isn't critical to the thought I would simplify to "the monkey who might be able to see my ears" or "can possibly see my ears". Otherwise AbouBenAdhem has the best option, though I might also suggest "The monkey whose ability to see my ears I'm wondering about"; splitting the prepositional phrase is more strictly proper but I think it reads a little better like this.