The payments watchdog is investigating the technical failures that have caused havoc at a number of high-profile outlets over the past week.
Greggs became the fourth large company to experience IT issues, after McDonald's, Tesco, and Sainsbury's.
The Payments Systems Regulator (PSR) stated that it was reviewing the incident.
"The PSR is aware of the recent payment issues and is assessing their nature to determine whether any further action is needed," the company noted.
The PSR is the UK's economic regulator for payment systems, ensuring that they perform effectively for individuals who use them.
If it discovers an issue with the payment system's resilience, it can refer the matter to the Bank of England.
These systems are receiving a lot of attention following a string of technological issues that prevented users from making purchases.
Sainsbury's was unable to fulfil most online food deliveries on Saturday due to complications with an overnight software update, which also affected contactless payments in shops. Tesco also had to cancel a "small number" of orders.
The day prior, McDonald's locations worldwide were unable to accept orders owing to a "global technology system outage".
On Wednesday, bakery company Greggs became the latest major retailer to experience IT system failures at several outlets.
Experts have suggested that the failures may be linked due to their near proximity, possibly through a shared network or payment infrastructure provider.
The CEO of the IT company Evolve, Alan Stephenson-Brown, stated that the many failures served as a timely reminder that even large corporations aren't immune to IT troubles.
“The retailers would have lost millions of pounds. This highlights that digital disruption is a principal risk for many retailers. Ensuring contingency planning is in place is vital," Mr Stephenson-Brown added.
The possibility for disruptions and vulnerabilities will increase as firms rely more and more on digital transactions, according to Jamil Ahmed, an engineer at the transaction provider Solace.
"The brick and mortar retail industry is facing a crossroads. Customers, accustomed to the constant uptime and reliability of online shopping, are demanding the same flawless digital experience from physical retailers," Ahmed said.