Owner Tony Johnston confirmed new plans for the Glassford Street branch and said he hoped to reopen in time for the Commonwealth Games.
As reported in later edition's of yesterday's Evening Times, the popular Merchant City deli - based in a category B-listed building - closed its doors without warning on Sunday.
Mr Johnston said: "We're refurbishing. We had planning permission about five or six years ago to do a boutique bed and breakfast and I've delayed it as there never seemed to be a good time to do it.
"There was always some problem, but a few things have happened of late that has made me think that it's now or never."
The deli and cafe is undergoing "minor" refurbishment on the ground floor and "major" refurbishment in the basement, Mr Johnston said.
Peckham's also has a branch in Byres Road, one in Hyndland Road and two in Clarence Drive.
One of the Clarence Drive premises is a specialist wine shop and the other a deli, which is closed for refurbishment and due to reopen in the summer, according to the Peckham's website. There is also a Peckham's branch in Edinburgh.
Mr Johnston said he was hopeful that the work in Glassford Street could be completed in time for the influx of visitors expected this summer for the sporting extravaganza.
But he added: "I would dearly love to be open again by the Commonwealth Games, but going from what we've experienced at Clarence Drive with the delays, I don't know."
Originally trading under the name Peckham and Rye, the first Peckham's deli opened at 43 Clarence Drive in 1982.