Are these sentences natural?
There are gossips going around.
There's a gossip going around.
Some gossips are going around.
There's a gossip going around that .....................

Question

Are these sentences natural?
  There are gossips going around.
  There's a gossip going around.
  Some gossips are going around.
  There's a gossip going around that .....................

Answer

I've never heard of gossip being made plural when it is used in this sense.

So I would say the following:
There is gossip going around.
There's gossip going around.
Some gossip is going around.
There's gossip going around that . . .

(The sense in which "gossips" is commonly used is when it refers to people who gossip a lot. For example, "The teachers in this school are a bunch of gossips!")