The PM is also expected to confirm that families will be able to form Christmas “bubbles” to allow visits across the four nations of the UK.
Some 90,000 Liverpool residents have been tested for Covid-19 since last Friday, with 430 people testing positive.
Move involves around half a million new, rapid turnaround tests.
In a short message released on Saturday Anderson urged people to "stick together and support each other and win this battle".
Liverpool mayor brands variations between regions under the same lockdown rules an "inconsistent mess".
Liverpool Walton MP Dan Carden said it was “difficult” to describe the “real strength of feeling across Liverpool at the utter failure of this government”.
"Boris and co have done nothing for the north," said the owner of the pub in New Brighton, Merseyside, following its closure under the tier 3 rules.
Steve Rotheram urged people to stick to "tier 3" local lockdown as he slammed "shameful" images of partying crowds.
The PM will later host a press conference at Downing Street to explain how each local area will be ranked on this new system.
Fireworks were seen hitting the Liver Building during celebrations on Friday evening, with fire crews called to the scene after a blaze started on the balcony.