The cabinet office minister warned of “difficult months ahead” but told BBC Breakfast he would not pre-empt scientific advice given to the government about whether more areas should be put in the toughest set of limitations.
London and several areas in the South East and East of England are already in Tier 4, which was first brought in ahead of Christmas amid fears about how easily the newly-identified coronavirus variant spreads.
“We review which tiers parts of the country should be in on the basis of scientific evidence,” Gove told the BBC on Monday.
“The Joint Biosecurity Centre will be making a recommendation to ministers, but I can’t pre-empt that because it obviously has to be a judgment based on the medical situation.
“As you quite rightly point out, the NHS is under pressure and these are difficult months ahead.”
Cases in the UK have been climbed above record levels within the last week, which has seen daily rises of more than 35,000.
The government has been investigating the variant, which could be up to 70% more transmissible and has now been found in other countries.
The government’s chief scientific adviser, Sir Patrick Vallance, said the variant accounted for 60% of London’s cases by December.
Millions of people in England – 43% of the country’s population – live in a Tier 4 area.
Restrictions in that bracket are effectively lockdown rules, with people told to stay at home unless they have a reasonable excuse to head out, like shopping for essentials or exercise, and non-essential retail must close.
It bans meeting people you don’t live with indoors and allows for meeting a maximum of one other person outside.
Those who gather in large groups face a £200 fixed penalty notice for the first offence, which doubles up to a maximum of £6,400 for repeated breaches.
Watch: More areas put into Tier 4