Ministers have been warning of a possible new wave of the virus this winter but are said to now fear it could come sooner.
A senior government source told the Daily Mail that the Prime Minister was worried by outbreaks “bubbling up” in the UK and abroad.
“The PM is extremely concerned by what he's seeing abroad and fears we could be seeing the same thing here in a fortnight,” they told the newspaper.
“He wants to go further on opening things up and getting people back to work, but he knows it'll be his head on the block if things go wrong.”
It comes after Mr Johnson warned on Tuesday that the UK must be "vigilant" as Europe suffers the symptoms of a second wave of Covid-19.
He hinted that quarantine restrictions could be imposed on further countries if a Covid-19 resurgence hits the Continent.
The Government is already embroiled in a diplomatic row with Spain after warning against all but essential travel to the country and its islands and axing it from its "travel corridor" list.
This means returning holidaymakers will have to go into isolation for 14 days in case they are harbouring coronavirus.
Mr Johnson defended the move and insisted ministers would not hesitate to act if outbreaks emerge in other destinations.
The Prime Minister said: “Clearly we now face, I’m afraid, the threat of a second wave in other parts of Europe and we just have to be vigilant and we have to be very mindful.
“What we have to do is take swift and decisive action where we think that the risks are starting to bubble up again.
“Let’s be absolutely clear about what’s happening amongst some of our European friends – I’m afraid you are starting to see in some places the signs of a second wave of the pandemic.”
With holidaymakers already facing uncertainty over trips abroad this summer, Mr Johnson said it was up to individuals to assess the travel risks.
“These are decisions for families, for individuals, about where they want to go,” he said.
The PM stressed that the quarantine measures were aimed at stopping cases being brought in to the UK, and could be expanded elsewhere if necessary.
He said: “It’s vital that when people are coming back from abroad, if they are coming back from a place where I’m afraid there is another outbreak, they must go into quarantine.
“That’s why we have taken the action that we have and we will continue, throughout the summer, to take such action where it is necessary.”