The Sunday Times of London reported the letters are set to go on display at the institution along with numerous Van Gogh works as part of a new exhibition titled "The Real Van Gogh: The Artist and his Letters."
The exhibition, which opens Saturday, represents the largest Van Gogh exhibition in England in more than four decades, the report said.
The estimated worth of the 63 Van Gogh paintings and 30 drawings on display in the exhibition is at least $4.8 billion.
Among the 40 letters featured in the exhibition is a letter Van Gogh wrote to his brother, Theo, a few days before Van Gogh took his own life.
"I'd like to write to you about many things, but first the desire has passed to such a degree, then I sense the pointlessness of it," the Dutch artist says in the 1890 letter.
"I'm trying to do as well as certain painters whom I've liked and admired a great deal," adds Van Gogh, who The Times said did not sell a painting during his lifetime.