Most publishing houses require that their authors obtain releases or licenses for their non-fiction books prior to publication of the book, to avoid the risk of a lawsuit arising from the content.
While publishing the facts, statistics and undisputed history of an NFL team is fine (and this includes the use of the NFL team name in the text), any photos that may be considered for use, as a way to illustrate the text, will generally be protected by copyright and will require the permission of the copyright holder prior to reproducing these photos.
And, as FlyingRon noted, there can be trademark rights issues that arise through the marketing of the book.
If you have approached a publishing house already and they have expressed interest in your work (and if this is not a self-publisher), the editor and the publisher will work to protect both you and themselves from suit by making sure all necessary releases are signed and in order.
If you are going the self-publishing route, it is strongly advised that you consult with an attorney well-versed in publishing law - and that you obtain writer's insurance enough to cover the costs of a lawsuit, should one arise from your publication despite your best efforts to avoid one.
Good luck.
