Officials have started private talks with groups representing major employers as ministers prepare a "road map" to avoid a second wave of Covid-19, the report said.
On Friday, Prime Minister Boris Johnson is expected to set out a fresh road map for his long-term strategy, which will include details of how the country will get back to work without risking a second spike, it said.
Face coverings inside shops are already compulsory in a few other European countries including Germany, Spain and Italy.
Johnson had said last week that tighter rules on wearing face coverings might be needed, while opposition Labour Party criticised his government for not moving sooner in England.
Monday's order noted that people who fail to wear face coverings may be fined up to £100 ($NZ192) in line with existing fines for people who do not cover their faces on public transport - which would fall to £50 if paid within 14 days.
Comments
When there weren't enough masks to go around, the official word from WHO was that masks weren't necessary or useful. Now there are enough masks available, suddenly the rule is the opposite. Is anyone out there idiotic enough to fall for this rubbish?