The 52-year-old was mauled by two dogs, believed to be XL Bullies, on Main Street in Stonnall, near Walsall, on Thursday. He is believed to have been defending his elderly mother from the dogs which attacked him.
Police are aware of videos circulating online which show Mr Price being attacked by the dogs.
A spokesperson for Staffordshire Police said: "We are aware that video footage of the recent dog attack in Stonnall where a man sadly died is now being circulated on social media.
"This was a horrendous incident and we understand that the impact felt by the local community is large.
"However, we would urge anyone with footage of the attack to not post or share it on social media for the sake of the victim’s family.
"It’s important that anyone with video evidence from this incident send it to us instead.
"Please call us on 101 quoting incident number 405 of 14 September.
"Alternatively you can message us using Live Chat on our website – orlo.uk/lFjXp or report anonymously via Crimestoppers on 0800 555 111."
A fundraiser for Mr Pirce's family has now surpassed £14,500. To donate, go to justgiving.com/crowdfunding/rob-ellwood