'The Jewel of Medina' was due to be published by Random House in the US, but was cancelled, because of fears of offending Muslim sensibilities.
Trykkefrihedsselskab's publishing company confirmed that an offer made for the Danish rights to Sherry Jones' book was rejected by her agent.
'Of course we are disappointed, but the most important thing for us is that the book gets permission to be published,' said Lars Hedegaard, president of the society.
It is unknown if other Danish publishers have been awarded the right to publish the book, but the author told a German newspaper that the book would be released in German and in English by October.
Helle Merete Brix of Trykkefrihedsselskab described the book as well written, but is worried about how some might react to the content.
'The novel describes the prophet getting a glimpse of the naked wife of his adopted son, and as a result sets his sights on marrying her. I don't really know how well that story will be received.'
The book was published last month in Serbia, but strong reactions from the religious community forced the publishers to pull all copies from the bookstores.