Deputy chief medical officer Professor Jonathan Van-Tam is expected to announce on Thursday, July 30 that the period will increase from the current rule of seven days.
Mr Hancock warned that a new spike in Covid-19 cases is “clearly” beginning to emerge in Europe as he said “we’ve got to do everything” to prevent it reaching the UK’s shores.
He hinted that Prof Van-Tam will announce the change for the self-isolation period for those with the key symptoms of a new continuous cough, high temperature or loss of taste or smell.
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Mr Hancock told Sky News: “I am worried about a second wave.
"I think you can see a second wave starting to roll across Europe and we’ve got to do everything we can to prevent it from reaching these shores and to tackle it.
“The measures that the chief medical officer will set out later are part of that, but so too are the measures we’re taking, for instance, to ensure that we don’t directly bring cases back to this country where there’s a big spike in cases.
“So, absolutely, on a second wave it is something I worry about and I worry about it because we can see it happening.”
But Mr Hancock also hinted that ministers are working on ways to reduce the current quarantine period for new arrivals to the UK from 14 days, amid pressure from the tourism industry.
He added: “We’re always looking at how we can have the least possible burden of the measures that we have to put into place so that is something on which we’re doing some work but we’ll only come forward with a proposal when we’re confident that it is safe to do so.”
It is not yet clear whether the self-isolation period for people with symptoms, which was introduced in March, will also be increased in Scotland, Wales and Northern Ireland.