I don't know if there is a single book on the 1940s NFL, but a few books come to mind that cover the period, and I'm sure others here will have more:
* "The League" by John Eisenberg covers the NFL from creation to the early 1960s, looking at the influence of five leaders: Halas, Mara, Rooney, Bell, Marshall. Probably a bit over 100 pages are on the 1940s, give or take. Well written and well reported.
* Several books on the Bears are heavy in the 1940s, including:
- Halas's autobiography
- "The Chicago Bears" by Howard Roberts, 1947
- "George Halas and the Chicago Bears" by George Vass, 1971
- "Papa Bear" by Jeff Davis, 2004
- "Bears vs. Cardinals" by Joe Ziemba, 2022
* Books on the NFL's ban on Black players cover this period, including:
- "Outside the Lines" by Charles K. Ross, 2001
- "Lost Champions" by Gretchen Atwood, 2016
- "The Forgotten First" by Bob Glauber and Keyshawn Johnson, 2021
* PFRA has two books on 1940s leagues:
- One on the AAFC, edited by Ken Crippen and Matt Reaser
- One one the minor league The American Association ('36-'41) and The American Football League ('46-'50), called "A Minor Masterpiece" by Bob Gill
Other items:
* Just looking online I see there is a book on the Steagles
* Woody Strode's memoir "Goal Dust" covers some of the period
* "The Genius of Desperation" by Doug Farrar (2018) covers a lot with Clark Shaughnessy and the Bears T
* In 1952, Roger Treat published the official NFL encyclopedia, and that has a ton of hard data on the period along with game summaries of the NFL championship game and the college all-star game
Lastly, I'll add one article by yours truly on Sid Luckman's 1943 season, which includes information on the impact that WWII had on the NFL:
https://www.windycitygridiron.com/2018/ ... ammy-baugh
Again, someone here might know a singular book on the period, but as a starting point, I recommend "The League" by Eisenberg. Great storytelling and characters, easy to read, good information:
https://www.amazon.com/League-Rivals-Cr ... 0465048706