Gollum tries to have Frodo and Sam killed by Shelob, so he could get the One Ring back from Frodo's corpse after Shelob would kill and "drink" him.
And Gollum is no stupid, so I guess he knows that Shelob is not interested in the One Ring (yeah, ok, spider means no hand, no fingers, so no place to "properly" put the ring on, but I can't believe the meaning/effect/power of the One Ring has such a material restriction as being wearable only by a human-like finger).
Why has she no desire to possess the One Ring? Even Gandalf, Galadriel and anybody else in the books seems to be tempted (or at least assumed temptable) by the One Ring, with the main exception being Tom Bombadil.
What makes Shelob different?
In the already existing questions the answers refer to Shelob just wanting to kill and eat everything (but not vegetables), so I can imagine another creature, other than Shelob, that only wants to kill pigs and eat pigs, probably a very insatiable hobbit. Or a troll. Are they also immune to the power of the ring?
The last paragraph is mostly a joke to say that I'm not really satisfied with Shelob only wants to kill and eat, so she's not interested in the One Ring.