"I want to be near to you" should be acceptable
Yes, I agree, so report it next time. But just for your information, the "to" is neither necessary nor very common. "Near you" is eight times more used than "near to you." Click here to see the comparison data.
'I wish I were near you' not accepted? I'll report it.
What about "I want to be around you"?
I'd say that has a slightly different connotation. What about "I want to be close to you?" Near is the synonymous with close to.
I this a common phrase in Finnish? Like, do people say this often when they miss their significant other?