I agree with SignOnTheWindow that it is part of the daily routine.
Personally I hate brushing my teeth (hate the sensation) but do it religiously twice a day because it is part of the daily routine (and obviously completely disgusting not to do so
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With my sons we always read a story at night before bed. If a child is reluctant to read themselves then just read them a story and ask a few questions like why does X feel upset or what do you think Y will do now? Basic stuff, lots of children pretend they don't know the answer but you have to say well look here when she says XXXX now do you see why she is upset? ie showing them that they cannot avoid the question.
I volunteer in a primary school that introduced a reading scheme which saw children finish books for the first time ever. I get reluctant readers who will tell me a book is boring but know that you have to read awful books to realise what a good book is. I tell them all that the better books are higher up the levels. 
Looking at the bigger picture, comprehension isn't just about reading a story book in primary school, it is about language, imagination, ideas for stories, story construction, learning to extract information from the text which is English SATs and then History, Geography, Ethics Religion and Philosophy etc as well as English in secondary school.
I still read to my mid teen son, he reads by himself but we like to share books in this family, I say we, Dh has read 1 book in the 20 years we have been married! Ds1 and Ds2 both teens read daily.
You have to try to find something they like, for Ds2 it was Beast Quest and Tom Gates - who I love. We have comic book style ones in school that seem to go down well.
Just read to your daughter, it is much easier to get the feel of a story if someone knows the correct tone of voice to use rather than decoding words.