He is not expected to provide exact dates for when the restrictions – first announced on 23 March – might change.
The new system will apply to England only but the government is working with the devolved administrations as they develop their own.
It is understood the system – with alerts ranging from green (level one) to red (level five) – will be similar to the one used to keep the public informed about the terror threat level.
Mr Johnson is expected to say England is currently at stage four but moving towards stage three.
The warning tool – to be administered by a new “joint biosecurity centre” – will also reflect the virus threat in different parts of the country, meaning the threat level in one city could differ quite widely from another.
This could inform the local alteration of restrictions in England.
A meeting of the government’s Cobra emergency committee involving the cabinet, devolved nations and the Mayor of London will be held before Mr Johnson’s televised address on Sunday evening, with the plans to be put before Parliament on Monday.
The prime minister is set to warn the nation that the UK is entering the most “dangerous” phase of the battle against the virus, according to the Sun on Sunday.
Speaking ahead of his address, he told the paper: “We’re past the peak now but we’ll have to work even harder to get every step right.
“Mountaineers always say that coming down from the peak is the most dangerous bit. That’s when you’re liable to be over-confident and make mistakes.
“You have very few options on the climb up – but it’s on the descent you have to make sure you don’t run too fast, lose control and stumble.”
‘Best protection is your front door’
Prof Jason Leitch, national clinical director for the Scottish government, told BBC Breakfast he “can’t explain” what the prime minister’s revised message of “stay alert” means.
Prof Leitch reiterated what First Minister Nicola Sturgeon said earlier this week – that the key message for Scotland “remains ‘stay at home'” – and added: “I think the messaging is really important…. the best protection for this virus is your front door. There isn’t any question about that.”
Speaking at the daily coronavirus press conference Mr Shapps said the move beyond Covid-19 would not be “a single leap to freedom” as he pledged £250m to improve cycling and walking infrastructure across England in the coming weeks.
Mr Shapps also refused to confirm if 14-day quarantines would be introduced for people arriving in the UK, saying he would wait for Mr Johnson to address the nation on Sunday.
Alert over protective goggles
Meanwhile, a model of protective goggles is being withdrawn from hospitals and care providers because they do not meet standards for coronavirus settings, the government has said.
A Department of Health and Social Care spokeswoman told the BBC it had issued an alert advising against the use of “Tiger Eye protectors” in clinical settings related to Covid-19.
The goggles were bought in 2009 and are now being removed from the supply chain, the spokeswoman added.
“The safety of health, care and all frontline staff is our top priority… we are arranging replacement stock for trusts who need immediate supply,” she said.
More than 70 public figures – including Baroness Doreen Lawrence and author Malorie Blackman – are calling for a full independent public inquiry into deaths from Covid-19 among people from ethnic minority backgrounds