A three-tier lockdown system is expected to be announced next week, with the worst-hit areas rated as tier 3 and facing the most severe restrictions.
Manchester, Liverpool and Newcastle are expected to be added to this group.
Mr Anderson told BBC Radio 4’s Today program on Saturday: ‘We had conversations with Downing Street yesterday, we had other conversations, discussions with them this afternoon.
“And I hope Liverpool will be one of those announced.
“We’ll be in the local lockdown, the new local lockdown, which is being announced, which will probably, well, be level three, and which will be enacted in parliament on Tuesday.
“We are continuing the discussions and conversations today. “
Level 3 measures should include the compulsory closure of reception areas such as pubs and restaurants, while mixing with other households will not be allowed.
Level 2 areas should also be hit by the ban on meeting people you don’t live with, although pubs and restaurants are allowed to stay open.
Places with the lowest infection rates will still have to adhere to the ‘rule of six’ and 10pm curfews currently in place in England.
The Mayor of Liverpool added: “We are now engaged in a conversation that tells us these decisions have been made, so it’s… a conversation, not a consultation.
“But the main point of the imposition of measures is clearly that: the imposition. We were not consulted. ”
Susan Hopkins, deputy director of the national infection service at Public Health England told BBC Radio 4’s Today program: “The picture shows that all over the country the number of cases is increasing.
“They are increasing faster in the North West, North East and Yorkshire and the Humber than in the South of the country.
“Regarding the aspects concerning the Northwest, it is that in certain pockets of the Northwest, it is increasing quite rapidly now in the over 60s.
“And this is the group of people who we know would need hospitalization more significantly than the younger population.