Mary Ragoobeer, 46, and her two sons Shane, 18, and Sean, 17, who lived in a flat in the destroyed building have been named as missing by the Leicestershire Police.
The Indian-origin owner of the affected building, Hardeep Singh, said that the Ragoobeer family had moved into the flat, above a Polish supermarket, around a year ago.
"I called Jose after I heard about the blast. He was at work and he was safe, but I don t know about the rest of the family. There was a gas boiler in the flat, in the bathroom at the back of the property, and a gas cooker," he told the Mirror .
Leah Beth Reek, 18, who is Shane's girlfriend, is also missing, as is 22-year-old Viktorija Ljevleva who is thought to have been working in the supermarket at the time of the explosion.
Police said: "Human remains relating to five people have been recovered from the wreckage but given the devastation caused by the blast and subsequent fire, it may be some considerable time before the bodies can be formally identified.
"The relatives of all five missing people have been informed and are being supported by specially-trained officers at this desperate time."
Matt Cane, Group Manager from Leicestershire Fire and Rescue Service, said that the focus of the work was now a search for any other human remains over and above those already recovered from the scene.
Despite the ferocity of the explosion on Sunday evening, and the intensity of the ensuing fire, there was always a slim chance that, if there had been someone else in the building at the time of the explosion, they may have been found alive," he said.
We cannot rule out the possibility of other people having been in the premises at the time of the explosion and whom we have yet to locate. While we have no intelligence to suggest this is the case, we cannot rule out that possibility until the search is over," Cane added.