It really depends on what you’re talking about.
I know of fictional telepathy that sends words. That does require a shared language to communicate well, although a recipient could remember the sounds and then find out what they mean later from people or books.
And, as in actual real-world dreams, meaning often uses the current reference set of the brain receiving the message. That is, we usually dream in symbols we already have in our brains, and/or our brains find symbols we have to represent what a dream’s message is, though our sleeping brains are often organized differently from our waking mind, such that we have dreams that make sense to our sleeping mind, but later our making mind has a hard time remembering the details, or when we do remember, has trouble making sense of what we do remember, or even remember how it seemed to make sense when asleep.
There are also fictional telepathic methods that talk about sharing consciousness, such that, at least temporarily, people know, think, and/or feel what the other person does (or what they send them), and this does not require language – it just sends feelings, impressions, or understanding. This might not require language. Or a person with this ability might learn to send ideas in a way that doesn’t require the recipient to use language to get the message.
Now, there are some stubborn people who will insist that meaning and ideas absolutely require language, but I would say that animals and insects routinely demonstrate this isn’t the case.
Then there’s also communication that people and animals do with body language, grunts, expressions, that clearly doesn’t require language, too. This is possible even without telepathy.
And there’s also communication possible, whether it’s telepathy or not, where you do what one communication course I took called “disappearing the space” between two people, where you just let go of your thoughts and separateness, and can just kind of have a shared experience where you’re not really sure who’s doing what, but you’re both on the same page. That’s not about language.
Language does generally require more precise communication, and confirmation, of details, though. I don’t know how to communicate “17.3 cm” (for example) using wordless rapport. (At least, not efficiently or without a ruler.)