The proposal for the book, titled Not That Kind of Girl: Advice by Lena Dunham, will feature essays from Dunham about a series of awkward and difficult moments throughout her life.
It was reported earlier this week that the Girls creator was in the process of shopping the proposal to various publishers, with the hopes of securing $1 million (£619,233).
The Hollywood Reporter now reveals that Dunham has met with five different publishers to discuss the proposal, and has thus far been offered $3.7 million (£2.3m) for her book.
Dunham is expected to make her final choice in the coming week.
Meanwhile, Girls is set for a return to HBO in January 2013.