This app was mentioned in 17 comments, with an average of 2.88 upvotes
Personal favourite for animal collecting has to be Disco Zoo. Sadly not updated, but a lot of fun whilst it lasts!
Linkme: Disco Zoo
Edit: https://play.google.com/store/apps/details?id=com.nimblebit.discozoo&hl=en_GB
Disco Zoo is pretty fun, doesn't pester about microtransaction crap, and progresses fine offline. The incremental aspect isn't particularly deep, but for a game that you can check back on every few hours or so to check your progress and play for a bit, I strongly recommend it.
Not exactly like Neko Atsume but I love animal games so here's some of mine:
List made using List My Apps
My wife's been hooked on this game
https://play.google.com/store/apps/details?id=com.nimblebit.discozoo
I don't know but I thought of Disco Zoo.
https://play.google.com/store/apps/details?id=com.nimblebit.discozoo
I've found it and I'm from sweden. https://play.google.com/store/apps/details?id=com.nimblebit.discozoo
It's still in the Google Play store:
https://play.google.com/store/apps/details?id=com.nimblebit.discozoo&hl=en_US
Part puzzle, part collecting, part management - and you get to throw an animal disco party.