All shops except pharmacies and food retailers could be closed by the Government under measures being considered by the UK's leaders.
Scotland's First Minister Nicola Sturgeon said retailers who were not providing "essential items" should shut their doors.
Sturgeon, who has been attending Cobra meetings where the UK's response to the coronavirus crisis has been co-ordinated, said too many people were still being expected to work as normal.
The Daily Telegraph reported that the closure of all shops except supermarkets, food stores and pharmacies could be announced by Boris Johnson at the daily Downing Street press conference.
The Prime Minister's official spokesman said: "We set out steps on Friday in relation to those premises which we needed to shut in order to reduce social interaction.
"But we've also said that we will continue to be guided by the science and by the medical advice, and if there's more that we need to do then we will do so."
A series of retailers have already announced they are closing their doors, including John Lewis and Primark.
The Prime Minister's spokesman said: "They are decisions for those individual companies to take.
"We keep all these measures under review and if there's more that we can do then that's what will happen."
Sturgeon went further, stating: "My message to shops that are still open is this and it is clear, if you are not providing essential items like food and medicines then please also close now."
She said that building sites and hair salons should also close.
"It has been clear to me that there are still too many people across our country who are being expected to, or expecting to, go to work as normal and this presents a serious and unnecessary risk of spreading the virus," the First Minister said.
"I want to reiterate that if you run a business and if the nature of your business makes it difficult for you or your workers to work from home or to practise safe social distancing then you should close."
