The Girls creator apparently wants $1 million (£619,233) for a book tentatively titled Not That Kind of Girl, a modern update of the work of Helen Gurley Brown.
A source close to Dunham told Page Six: "Instead of just auctioning off the book to the highest bidder and having them publish it, they are doing it in a unique way.
"The top five bidders in this week's auction will sit down with Lena on Friday for a meeting. She'll then choose from those offers."
Dunham's representative has not commented on the report.
The writer-actress recently earned four Primetime Emmy Awards for the first season of her HBO series Girls.
Girls kicks off its second season in January 2013.