There is no offline version of Jisho specifically, but there are offline apps that use the same data sources. Some of them are listed in our FAQ: https://jisho.org/faq
If you want to make your own app you can see our list of data source on the About page: https://jisho.org/about
sounds like you are looking for yomichan https://github.com/FooSoft/yomichan
It's highly customizable and you can add whatever dictionaries you like to it. You probably want to install jmdict, which is the main dictionary used by jisho. I also have 新明解 and 大辞林 on mine, which I like a lot
you can use the build of jmdict on the yomichan page, or you can use yomichan-import to compile the latest build at your own leisure, which is what I do (jmdict is constantly being updated!)
also here are a bunch of dictionaries in addition to the ones listed on the yomichan page. some of them have occasional formatting issues, but for the most part they are very useable https://learnjapanese.moe/monolingual/#getting-and-using-monolingual-dictionaries
enjoy!
Offline access/version?
Would there be a possibility, to allow 'downloading' some parts of the database/store to make offline usage available through some kind of application which reads that data? I'm a dev and Japanese learner without internet connection sometimes, so I'd like to make some sort of offline dict.