The senior Cabinet minister said the government was looking to allow “intimate contact” as part of the next stage of the road map for lifting lockdown.
Boris Johnson is expected to announce in a Monday press conference that stage three of the lockdown lifting can go ahead as planned on May 17.
It means pubs, restaurants and cafes can open inside, and other venues such as cinemas will be able to reopen.
Overnight stays at other people’s homes will also be allowed, with groups limited to six people or two households, if the group is bigger than six, indoors.
Asked if there would be an end to the ban on hugging, Gove told BBC One’s Andrew Marr Show: “Yes, all being well, the prime minister will confirm tomorrow that there will be a relaxation.
“We have already indicated a proportionate relaxation on international travel – very, very limited at this stage because we have to be safe.
“And in the same way as we move into stage three of our road map it will be the case that we will see people capable of meeting indoors.
“And without prejudice to a broader review of social distancing, it is also the case that friendly contact, intimate contact between friends and family is something that we want to see restored.”
Asked if from May 17 hugging would be allowed, Gove replied: “Yes.”
The shadow Cabinet Office minister also revealed that the government was involved in “delicate negotiations” on holding football’s Champions League final in the UK, rather than Turkey, which has been put on the travel red list.
The final will be contested between two English clubs, Manchester City and Chelsea, on May 29.
The head of the Oxford University vaccine group agreed that it was the right time to ease restrictions in England.
Professor Andrew Pollard told Marr the country has seen the “extraordinary success” of both the vaccination programme and the “prolonged” lockdown.
“I think it is time to start, based on the very careful modelling that’s been done, relaxing some of those restrictions,” he said.
“That means we’re in a very fortunate position here in the UK.”
Gove told Ridge on Sunday on Sky News: “My son is a Chelsea fan and he would dearly love to see the game played in the UK.
“But there are delicate negotiations that are going on at the moment.
“My friend, my colleague the culture secretary Oliver Dowden, is talking to people about this at the moment and so I don’t want to cut across that, but I’m sure that fans in the UK would dearly love to see the final played here in the UK.”