There were many reports claiming that people have memorized the entire bible. For example:
15 years ago, Baptist Press released an article reported that Nadine Hammonds, a blind woman, has memorized the New Testament
Nadine says it took her about three years to get the memorization done. She had memorized Scripture all her life, so she did have a history of Scripture knowledge, but her goal of memorizing the whole New Testament only took shape the last few years.
In 2007, Church & Ministry reported that Charles Matlock, 59, is known as the “Walking Bible of West Tennessee” has memorized most of the Bible and uses his gift to preach as a traveling evangelist.
Matlock said he started to memorize the Scriptures when he was 12 years old. He recalled memorizing his homework one day and thinking to himself that he could also memorize Scripture.
Dr. William Evans wrote a book called How to Memorize the Bible in 1919. It is reported:
Dr. Evans memorized the entire King James version of the Bible plus the New Testament of the American Standard Version.
The site also has two chapters teaching how to memorize the bible by Dr. Evans:
Although written in 1919, Dr. Evans’ scripture memorization techniques are still used today. Most books and websites that attempt to sell memorization techniques are largely using Dr. Evan’s ideas.
His techniques for memorizing the Bible are simple, clear, practical and have immediate benefit. They work regardless of your age.
The most famous person who is said to have memorized the entire bible is Jack Van Impe:
Regarding his extraordinary memory in regard to Bible verses, Van Impe has said that he has memorized 14,000 verses, and that it took him 35,000 hours to do so.
Jack Van Impe recites has own website also along with methods:
Eager to have others memorize the Bible, Dr. Van Impe has been willing to share the method that has made him "The Walking Bible."
First, he prepares index cards with Bible verses on one side and the references on the other. He generally prepared 50 cards at a time. Others might not want to make that many. The important thing is to get a start with some set number of verses.
He suggests choosing verses by subject or doctrine, not by chapter. At one time, he tried memorizing by chapter, but found himself less able to use the verses quickly. He would lose valuable time working through a number of verses to get to the one he needed. Memorizing by subject or doctrine is more liable to bring verses to mind when a given subject is raised.
It is also reported that John Goetch the Executive vice president at West Coast Baptist College has memorized over 14,000 verses and still does one per day as he is running his 5 miles at 5:30 A.M:
As an added bonus, a special section devoted entirely to the subject of memorizing scripture is included. Dr. Goetsch has personally committed over 14,000 verses to memory.
He also has a book on amazon (called: Homiletics from the Heart: Preaching God's Word God's Way) explaining his methods of memorizing the bible.
How To Memorize The Entire Bible In No Time Flat is a book by Adam Houge teaching how to memorize the entire bible.
9 Months ago, is has been reported by the Baptist Press also, that a pastor memorized 35 books of the bible.
But Davis, pastor of First Baptist Church in Durham, N.C., will tell you there is one book that has captured his heart; it is the Bible. And his desire to know God's Word has led him to memorize 35 of its books.
Those reports claiming that some people have memorized most if not all the New Testament of the Bible are weak evidence.
From a skeptical point of view, the question of "Has anyone memorized the whole Bible?" might be provable but is definitely unfalsifiable since it cannot be contradicted by an observation or the outcome of any physical experiment.