ᐅ Gurgling noise in the drain

Hello, I am new here and not sure if this is the right forum for my question. If not, please let me know!

We recently moved into an old house from 1960 and will soon be getting a new kitchen.
The problem is that with the old kitchen, whenever water runs from the sink, the drain makes a terrible gurgling noise.
I believe the sink is not properly vented.
The previous owner said it has always been like that and it didn’t bother him.
Well, it does bother me a lot, and I am thinking about what can be done.

The easiest solution, I thought, would be to install some kind of vent in the sink drain, behind the P-trap in the drain fitting...
Does such a thing exist, and what can I do about unpleasant odors?
How can I tell if there really is no vent without opening up the walls? There is no vent pipe visible near the roof... and not elsewhere in the attic, and otherwise, we don’t have gurgling problems. How was venting done in older houses?

Who can help me?

Best regards, suxxi

Check the attic to see if there might be a pipe ending under the roof.

We don’t have an attic; the rooms extend up to the roof. (wood paneling, insulation * 😕*, roofing felt, tiles) If anything, the pipe can only end directly under the tiles... and there are a few inaccessible corners behind the knee walls... but you can’t get to them without a hammer. 🙁