The 49-year-old singer expressed her wish during an interview with NME for their tribute to her late husband. The Nirvana frontman committed suicide almost twenty years ago on April 5, 1994.
Love said that she and daughter Frances Bean Cobain have been "swarmed" with fan mail and social media posts that ask for the musical to become a reality.
"Frances and I have thought long and hard and agreed that if we can reach up to the highest shelf and select a team of the greatest and most respected writers, producers and directors, then a Broadway musical is very likely to happen," the singer revealed.
"There would have to be a story, and a great story, one that hasn't been told before," she continued. "I would devote countless hours with an A-team to create a project that reflects Kurt in the most respectful but honest way possible."
Love expressed her desire to "resurrect" Cobain's story, music and legacy "not only for the world to see, but more importantly for our daughter to see."
"I know her father's spirit will be on that stage," Love said. "Sitting in that theatre with her will be the most emotional experience of our lives."