The End of the Tour centres on a road trip Wallace, who committed suicide in 2008, took with Rolling Stone reporter David Lipsky in 1996, and is based on the book Although Of Course You End Up Becoming Yourself: A Road Trip With David Foster Wallace.
The movie is currently filming, but the family is not on board with the project and insist Wallace would never have consented to it.
A statement from a representative for the estate reads: "The David Foster Wallace Literary Trust, David's family, and David's longtime publisher Little, Brown and Company wish to make it clear that they have no connection with, and neither endorse nor support The End of the Tour.
"This motion picture is loosely based on transcripts from an interview David consented to eighteen years ago for a magazine article about the publication of his novel, Infinite Jest. That article was never published and David would never have agreed that those saved transcripts could later be re-purposed as the basis of a movie...
"The individuals and companies involved with the production were made keenly aware of the substantive reasons for the Trust's and family's objections to this project, yet persisted in capitalizing upon a situation that leaves those closest to David unable to prevent the production. The Trust will continue to review its legal options with respect to any commercial exploitation of the motion picture."