I know of an app which offers such books. I have been using it since last year and I like it a lot. It offers a variety of books of different categories. It has a library section and a bookshelf section. In the library section the book is downloaded easily and saved in the bookshelf section. In the bookshelf section, you can read your book offline. It also does not close the page you are in saving the time you would looking for your page when you go back later. It calculates for you where you have reached and therefore helping you to keep up the pace of reading.
This app is known as Anybooks. You can download it freely from play store or apple store in your phone.