In the Gaura-ganoddesa-dipika, a book written by Kavi-karnapura that describes all the associates of Sri Caitanya Mahaprabhu and who they previously were, there is the following statement regarding Narayani:

When Lord Krsna was a child, He was nursed by a woman named Ambika, who had a younger sister named Kilimbika. During the time of Lord Caitanya's incarnation, the same Kilimbika used to eat the remnants of food left by Lord Sri Caitanya Mahaprabhu. That Kilimbika was Narayani, who was a niece of Srivasa Thakura's. Later on, when she grew up and married, Srila Vrndavana dasa Thakura was born from her womb. A devotee of Lord Sri Krsna is celebrated in terms of devotional service rendered to the Lord; thus we know Srila Vrndavana dasa Thakura as the son of Narayani. Srila Bhaktisiddhanta Sarasvati Thakura notes in this connection that there is no reference to his paternal ancestry because there is no need to understand it.