It comes after firms such as B&Q have reopened their doors to shoppers, while John Lewis has said it hopes to reopen all its shops next month.
Proposals from retailers came after Boris Johnson urged the public to stay at home in order to avoid a second peak in infections, which could further weaken the economy.
Greggs said it plans to reopen a small number of stores for takeaway and delivery next week after shutting all its sites due to the pandemic.
The boss of the bakery chain has told staff it plans to open 20 stores in the Newcastle area from Monday May 4 as part of a ‘controlled trial’.
Roger Whiteside, chief executive of the business, said he hopes the trial will inform the business about what changes need to be made to operate safely and meet social distancing guidelines.
He said he believes the trial, which will involve a limited product range and shorter trading hours, will take at least two weeks.
In a letter to staff, Mr Whiteside said he hopes to open around 700 stores, including 150 franchise shops, with new operational measures in place from June 8.
‘We expect it will only be possible to open this many shops if the Government has taken a first step in relaxing the lockdown, which could be to open the schools,’ the chief executive said.
‘This timing may change depending on future Government announcements.’
The company predicted that sales in the stores will be ‘significantly lower than normal’ while social distancing measures are in place.
Mr Whiteside said it then intends to open all of its 2,050 stores by July 1, when the Government's current furlough support package is due to end.
A Greggs spokeswoman said: ‘We want to play our part in getting the nation back up and running again, so we are planning to conduct a limited trial with volunteers to explore how we can reopen our shops with new measures in place that keep our colleagues and customers as safe as we can when we re-open at scale.’
Rivals such as Burger King, Pret a Manger and KFC have already reopened a small number of sites for takeaway and delivery.
Meanwhile, it is understood that Leon is due to re-open six of its restaurants for delivery and click-and-collect, in addition to the 16 it has kept open to sell groceries.