“I am begging you to consider what use some of these reports are serving, other than to cause further harm to everyone left behind picking up the pieces. Before you leave comments or make videos, ask yourself if you would like your child or family to read them.
“Please give Liam the little dignity he has left in the wake of his death to rest in some peace at last.”
It comes as Payne’s girlfriend, influencer Kate Cassidy, shared a statement online about the loss of her partner.
In 2016, Cole and Payne made their public debut as a couple on the red carpet at the Global Gift Gala in Paris.
A year later they welcomed their baby boy, Bear.
Payne announced his joy about becoming a father, saying in a statement that he was “incredibly happy”.
“It’s a moment that I will never forget for the rest of my life and my favourite memory I have so far. I’m completely in awe of his incredible mother and how she has been the whole way through this, she’s really made my dreams come true,” he wrote on social media.
Local newspaper La Nacion reported Payne, 31, was found dead after falling from the third floor of the CasaSur Palermo Hotel, citing emergency services.
Witnesses told local media Payne had fallen from the balcony of his hotel room shortly after 5pm on Wednesday local time, AFP reported.