My son was the same when he was young and non verbal..now he is the best reader in his class (5th grade and reads 400 pages or more a week) and his vocabulary is amazing from reading.
First I think my son saw me reading as the book taking away from the attention he was trying to get and later he saw reading not as mommy looking in a book away from him but a time we connected using the book once he started following the story.
Level books tell you once they start reading the reading comprehension level of the book..in the beginning more important is short stories that we could start and finish in about a 15 minute session. He wanted to hear the end of a story or couldn't disconnect from the reading time. Good old fashion short bed time story or a fairy tail book with bright pictures.
A book with a lot of pictures. Read and show pictures..the pictures help so much for them to follow the story and understand it was a story adventure we were going on together. Be animated when your reading so its fun. He would love and help pick out "pretty picture" books with me once he got into it.
I put up book shelves high on his walls to physically surround him with beautiful colorful books so they became something he did not fear but something part of his world. He would tear up books if left down or in the beginning so the prettiest books were special reading when he would learn to handle the special books more careful once he understood but I bought used books so if he destroyed it no stress no harm.
I shopped at good will used book stores, amazon used books, ebay etc.... once he could request special books we used trips to a book store but not until he was to the point he wouldnt go in and tear up all the books in the big book stores because so many books was overwhelming and new books so expensive.
It is much easier to give a kid a computer or tablet so I make sure reading is always something he has at his finger tips now and electronic enjoyment is given to him in small measures or he wouldn't continue to read.
Don't give up...my older kids were honor students and graduated honor college. Even with them reading was something we worked and built on..with George it has been more work but so much more rewarding. His book is also a tool to cope with the stress in school when he is on a playground or with other kids he cant socially interact with. He does obsess about reading and gets in trouble for pulling out his book when he should be listening to the teacher but that is a small problem the teacher helps us with. So just don't give up and make it a part of a routine you do every night. At bedtime George had less energy to fight over it. Make sure your books have lots of pretty pictures now and when she reads move to the level books for her ability.

Books... Not at all, the moment I open a book to read to my 4 year old son, he quickly turns pages and closes the book. I can't get his attention to read it. His speech therapist is trying reading to him with the photos to match on the page - interactive way. But for me at home, I m still figuring out the same.

Our son loved books and lost interest between ages 2-3. Our therapist used Velcro and laminated little pictures and had him match the picture to the page. For example in the Brown bear book he would match yellow duck to yellow duck. You can do it with $1 board books. Sensory touch and feel and lift flap books helped. He needed a hands on activity to keep him engaged. He was rewarded for sitting during circle time and answer questions about the book. Our new therapy has him lead. He flips through the book. We might say "I see a duck." He starts pointing out things on his own. He chooses books from the library. School uses stories that he likes to teach print awareness and reading. It helps to talk about the picture and get him engaged and only read the entire story if it is simple rhyme type of story. I can read books are nice and simple but still "big kid" books. We read while he eats. it is regulating. A speech therapist got him interested in "Goodnight Gorilla"and helped him tell the story by slowly removing verbal prompts. "The Gorilla is walking." The Lion is(our son said 'Walking." The Our son said "Armadillo is walking ". We would eventually point and he enjoyed telling the story.

My son did the same thing when he was a child. My heart goes out to you because it is frustrating. I would suggest that you start to familiarize yourself now with Pecs communications. Point to the pictures and explain instead of reading the words maybe for now. My son does read now but I did wonder if he ever would. be positive and don't give up.

Nope. Won't let me read to him. I asked him about it and he said that I read too slow. Turns out he was reading to himself and my voice was interfering with his ability to concentrate. Make me sad a little - I always dreamed of special time with my kiddo, snuggled up together, reading a story. We still snuggle up, we're just each reading our own book.