That would allow people to meet up inside homes, initially in groups of four people from two households. Cinemas and children's play areas will also be able to reopen.
"Friendly contact, intimate contact, between friends and family is something we want to see restored", Gove said.
According to the PM's roadmap out of lockdown, next Monday will see hospitality venues reopen for indoor services, a lifting of a number of social restrictions and even global travel will once again be permitted.
The government has said the latest data suggests easing restrictions from 17 May is unlikely to risk a resurgence in infections.
In comments released by No. 10, ahead of a press conference on Monday at which Johnson will confirm the move, the United Kingdom prime minister said his roadmap out of lockdown remained "on track".
The Office for National Statistics estimates that 1 in 1,180 people have COVID-19, down from 1 in 480 at the start of April.
"The Roadmap remains on track, our successful vaccination programme continues - more than two-thirds of adults in the United Kingdom have now had the first vaccine - and we can now look forward to unlocking cautiously but irreversibly". But the UK's successful vaccine rollout has already administered first jabs to more than 35 million people.
The government said infection rates are at the lowest level since September and hospital admissions and patients continue to decrease, or plateau at low levels in some areas, with levels similar to July previous year.
More than 127,000 people have died of coronavirus in Britain, the highest toll in Europe.