Depends on how you define "nosy".
When it comes to knowing as much information and details as possible, I'd say Te HA - "to know" - is the winner.
For example, my SEE sister is the nosiest person I've ever known. She reads text messages of our mother, has read in my diary before, etc etc. She just wants to know it all. There are no boundaries to her curiosity.
I think Te is the most curious in terms of factual information. Te leads can be very curious/nosy as well. I've found Te leads collect information and facts like Pokémon, and that can make them nosy.
After Te leads comes Te Demonstrative (+Ne). So basically, ILE. My ILE brother is also very curious about... stuff, haha, including my own privacy, too.
Ne is curious when it comes to ideas, so EII and LII can also be quite curious or even nosy, but they usually respect other people's boundaries too much or won't push anyone so practically they are not too nosy.
Fe is curious about other people, and again, it depends on how you define nosiness. My ESE mother is very interested in what the kids of her friends are doing and so forth, basically how people's lives are going, but differently from other people I've known she does not pry... as much.
All in all, I'd say the nosiest people are Exxx.
To be more specific: ExFx > ExTx