nose in a book, have one's - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Be constantly reading, as in Walter is known for having his nose in a book. This expression graphically depicts immersing oneself in reading. [Mid-1900s]