Some Ministers are said to be against ending the lockdown to early to avoid a second wave, while others want to lift it to avoid a bigger economic crisis.
Mr Johnson had stressed back in March he expected the country to be able to “turn the tide” in 12 weeks.
Now recovering at Chequers after being released from hospital a week ago, the PM is considered one of the “doves” who oppose lifting lockdown early.
At a meeting at the retreat last week, the PM is believed to have warned ending the lockdown early could damage the economy and people’s health.
He is believed to be backed by his chief adviser Dominic Cummings, who believes Britain should be cautious until it knows more.
Mr Johnson is still not working, but instead getting daily updates from his team.
He is joined by Health Secretary Matt Hancock, who also contracted the virus.
Mr Hancock has repeatedly backed the lockdown, to ease pressure on the NH and get the transmission rate as low as possible.
The senior Minister has also tried to avoid discussing an exit strategy over fears it might cause people to break the rules.
The “hawks” are those more worried about the economic impact of a long-term shutdown and want to ease restrictions sooner.
This is said to include Chancellor Rishi Sunak, the Trade Secretary Liz Truss and Cabinet Office minister Michael Gove.
Mr Sunak is believed to have been calling for an end to the lockdown as quickly possible to limit damage to the economy, and said he was “deeply troubled” by the viruses impact last week.
The Home Secretary Priti Patel is also believed to be in the Hawk camps, being concerned by an increase of nearly one third in reports of domestic violence.
The Foreign Secretary Mr Raab, Leader of the House Jacob Rees-Mogg, Education Secretary Gavin Williamson, Business Secretary Alok Sharma and Pensions Secretary Therese Coffey are said to be undecided.
On a call last week Mr Sharma warned lifting the lockdown too early could bring further setbacks to business because of a second peak and said “that’s the worst possible thing you could do”.
Britain has been in full lockdown for four weeks so far – since March 23 – and is due to have another two weeks of shutdown at least.
Scottish First Minister Nicola Sturgeon said some plans to lift some lockdown measures could be set out this week.
She said earlier that their aims will be to suppress the virus while restoring some kind of normality, adding: “We will need to learn to live with this virus.”
It came as the UK announced 449 more coronavirus deaths taking Britain’s total death toll to 16,509.
It is the lowest daily number for a fortnight, since April 6 when 439 victims were confirmed.