The outlet says a video shows how one woman was ordering the last roll at the counter when the other rushed up to her and punched her in the head, before one of them was pushed to the floor and kicked.
"According to witnesses, the fight broke out over who could have the last vegan sausage roll that was available," writes The Tab.
Greggs vegan sausage roll
Greggs launched its vegan sausage roll in January, capitalizing on the Veganuary hype. It was initially available in around half of Greggs' 1,950 stores.
The product, which gained huge attention across social media as well as the mainstream press, went onto become the fastest selling new product Greggs has launched in six years.
"With all the hype surrounding it, it sold out straight away and we have 900 shops who didn't get it who are screaming out for it, so we are chasing our tail getting availability running," Greggs Chief Executive Roger Whiteside, said shortly after the launch.
"We didn't know if it would sell or not. Now we know it's selling out we need to get it out there. The priority is to get it into existing shops, and then the other shops who didn't get it will get it. We are pulling out all the stops to get it out there as quickly as possible."
Greggs confirms incident
"We can confirm that there was an incident at our shop on Gordon Street, Glasgow," said a spokesperson for Greggs.
"The safety of our colleagues and customers is extremely important to us, and we are cooperating with the police as they investigate the matter."