A rift opens in space, dumping an alien (or several) on our world from another reality close by. This alien is an amorphous, green blob the size of a small cat with no separate internal organs, just even goo, but it does have a rather large appetite. The world it came from is crude, it being one of the higher in the food chain there. It's diet normally is insectile in nature, but here... for whatever reason, women seem to entice it. A curious coincidence in pheromones, tastes and smells.
It will attempt to envelop it's prey and hide away as it consumes it's meal, though it has no understanding of a modern society and cities so might easily be confused by the urban sprawl, making it's efforts to hide... erratic to say the least.
It isn't sapient (to begin with) having roughly the intelligence of a dog, but it has very different biochemistry from Earth life and it eating such life can have odd results. It gradually getting smarter (and larger) after eating it's fill is possible, so is it accidentally merging with what it eats instead of digesting it. It could also find itself sucked inside someone, given it's size, and end up messing with the human's nervous system. It also could end up being messed with by someone's nervous system, changing it's consciousness based on the host's mind... or perhaps even their subconscious mind or dreams.
The Slimes are drawn to women, but could also eat (or absorb, or be absorbed by) men too. It's just not what they are mainly focused on. They certainly seem to vastly favor women over men in taste. This could lead to a male main character (either merged with or affected by the slime) to go after various other women 'meals.' However if this happens they will become even more focused on the female of the species.
They also can release pheromones, causing extreme sexual arousal in those around them. This originally was to distract the prey while they ate, but if they get confused with humans it might end up with just a free for all play time with this. Not all slimes use this to a large degree, depending on what kind of predator they were on their home world. Stealth predators often won't to avoid drawing more prey than they can deal with into an area.