Payments Systems Regulator is examining spate of outages, which also affected Sainsbury's and Tesco
The payments watchdog is examining the tech outages that have caused chaos for a number of high-profile retail outlets over the last week.
Greggs became the fourth major firm to suffer IT issues, following problems at McDonald's, Tesco and Sainsbury's.
The Payments Systems Regulator said it was reviewing the situation.
"The PSR is aware of the recent payment issues and is assessing their nature to determine whether any further action is needed," it said.
The PSR is the UK's economic regulator for payment systems, seeking to ensure they work well for those that use them.
Sainsbury's could not fulfil most online grocery deliveries on Saturday due to issues with an overnight software update which also hit contactless payments in stores.
On Monday, bakery chain Greggs became the latest major retailer to see its IT systems fail in some stores.
As a result of the outages being so close together, experts have suggested they could be linked, for example via a common network or payments infrastructure provider.
Sainsbury's deliveries cancelled over tech issues.
All of the bakery chain's stores hit by an earlier technical glitch are now trading as normal, Greggs says.