But more than 30 years since his death, nobody has dared to incinerate the manuscript, a collection of 50 index cards that is languishing in a Swiss bank vault.
Dimitri Nabokov, his sole surviving heir, has carried the burden of what to do with it since 1991 when his mother, Vera, died, having never been able to bring herself to dispose of it.
For years Nabokov, who is the only living person to have seen the entire manuscript, has tantalised his father's fans with his descriptions of it as a distillation of the writer's output and the most "brilliant, original and potentially radical" script he ever wrote.
Now 73, the former opera singer, who has kept the literary world guessing for years, has delivered the strongest indication yet that he is prepared to put a match to the manuscript.
In an email and telephone exchange with the US literary critic Ron Rosenbaum, Nabokov has stressed that he wants to spare it the harsh treatment that his father's novel Lolita received at the hands of critics.
Lolita, which is commonly viewed as one of the most controversial novels in modern literature, tells the story - depending on your point of view - of a pre-teenage temptress who destroys the life of a professor, or an innocent child who falls victim to the lust of an ageing sex maniac.
According to Rosenbaum, who agreed not to quote Dimitri Nabokov directly, he "admits to feeling protective about Laura", particularly "in light of the treatment of his father's works by certain writers he regards as deeply misguided in their 'psychological' analyses of Lolita and other works, analyses he characterises as virtually criminal idiocy".
Rosenbaum points to Dimitri Nabokov's particular concern about those he refers to as the "Lolitologists", or the critics who have read into Nabokov's works suggestions that the author himself was molested or abused.
Writing on the US online magazine Slate, Rosenbaum says: "The desire to spare Laura similar molestation by the Lolitologists inclines him to obey his father's wishes and consign the manuscript to oblivion."
Nabokov fans are split on the issue, with some fearing they will never set eyes on a manuscript - referred to by the writer's son as "the most concentrated distillation of [my father's] creativity" - that could throw fresh light on the writer.
They argue that if the author had really wanted it destroyed he would have done it himself. They cite the examples of writers such as Kafka and Virgil, arguing that the literary world is much richer for the fact that their wishes for their works to be destroyed were ignored.
Others, though, say Nabokov's wishes should be respected.
Rosenbaum fronts a growing band of critics who want the son to bring an end to the dilemma, appealing to him, "please don't continue to tease".
"Dimitri, with all due respect, I think the time has come to make a decision," he wrote in Slate.
"Tell us why you think it's the distillation of (your) father's art ... Or give us Laura ... Or put us out of our misery and tell us that you intend to preserve the mystery forever by destroying Laura."
The Nabokov scholar Zoran Kuzmanovich, who was one of a chosen few to hear the writer's son read an extract from Laura several years ago, reported that it was "vintage Nabokov".
"It sounds as though the story is about ageing but holding on to the original love of one's life," he said.