The chain currently offers vegans potato wedges, mince pies, and soya milk for hot drinks.
But animal rights charity PETA wants it to create a plant-based version of its classic grab-and-go pastry snack - something the chain reportedly says it has been working on for years.
PETA Director of Vegan Corporate Projects, Dawn Carr, said: "More people than ever are clamouring for healthy vegan options from their favourite on-the-go eateries.
"PETA is calling on Greggs to heed this growing demand, add a vegan sausage roll to the menu, and watch the cruelty-free treats fly off the shelves."
According to PETA, it has documented that in the UK meat industry, farmers clip or grind down many piglets' teeth and cut their tails off without any painkillers.
A spokesperson added: "After female pigs give birth, they're confined to farrowing crates so small that they can't even turn around, let alone fulfil their strong urge to build a nest as they would naturally do.
"They're forcibly impregnated over and over again, and each litter of piglets is torn away from them after only a few weeks and transported to fattening pens before eventually being sent to slaughter."
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