Have your nose in a book is often used to describe someone who is always reading and at the same time is absorbed in the activity. You might like to look at another exercise I've done on idioms using other parts of the body:
Hi,Have your nose in a book is often used to describe someone who is always reading and at the same time is absorbed in the activity. You might like to look at another exercise I've done on idioms using other parts of the body: