The former One Direction star - who died earlier this month at the age of 31 after falling from a hotel balcony in Buenos Aires - finished filming Building The Band for the streaming giant just months before his tragic passing.
While the launch of the series has "definitely not been shelved", the corporation will meet with his family to discuss a potential release at some point in the future.
A source told The Sun on Sunday newspaper's Bizarre column: "it is too soon to make a decision, but the show has definitely not been shelved.
"Filming was completed at the end of summer.
"Netflix will sit down with Liam's family when the time is right to speak about the series and when it could be released."
The insider noted that the death of the singer had left everyone "devastated" at the company, and they had decided that there was no pressure to release the series bur were hoping that it would become a "beautiful tribute" to the star when it did come out.
"Everyone involved is devastated and their heart goes out to his family. There is no rush or pressure to release the series.
"It would simply be a beautiful tribute to Liam and capture him at his best in the months before his death."
On the show, Payne served as a mentor alongside Pussycat Dolls singer Nicole Scherzinger - who initially chose him to be a part of One Direction on the UK version of The X Factor in 2010 - and Destiny's Child star Kelly Rowland as they oversaw 50 wannabe stars competing for the chance to be in a band.
Payne shot to fame alongside Niall Horan, Harry Styles, Louis Tomlinson and Zayn Malik and they went on to achieve global chart-topping success.
The group went on hiatus in 2016 and Payne went on to have son Bear, seven, with his former partner Cheryl and enjoyed a solo career with his hit single Strip That Down and his only album LP1.
He had travelled to Buenos Aires with his girlfriend Kate Cassidy to see his former bandmate Horan perform in the city, but they decided to stay for a couple of weeks and she left just days before his death.
Just over 24 hours after the tragedy, the One Direction singers released a joint statement, admitting to being "devastated by the news of Liam's passing".
"The memories we shared with him will be treasured forever. For now, our thoughts are with his family, his friends, and the fans who loved him alongside us," they said.
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