Sandwell, Walsall and Birmingham will be the focus of the discussions but other areas could be included, a West Midlands Combined Authority briefing was told.
However it has since emerged that the Government is now considering implementing a new national lockdown for England from as early as next week.
Under Tier 3 social mixing is banned both indoors and in private gardens, while pubs and bars must close unless they can operate as a restaurant.
Clive Wright, regional Covid-19 convener, said that infection case rates in each of the three local authority areas are now either inside or above the key “threshold” of 250 to 300 cases per 100,000 people.
For the week to Monday - the latest period that full data is available for - the infection rate in Walsall was 336, Sandwell 318 and Birmingham 276.
Mr Wright added there was also a case to include Wolverhampton (251) and Solihull (229) in discussions, where rates are slightly lower but rising.
Staffordshire is not expected to be included despite South Staffordshire (401) and Cannock Chase (343) having the two highest infection rates in the region.
Latest Covid-19 infection rates
The latest rolling seven-day infection rate of Covid-19 by local authority area, compared to the previous week.
The figures are for the seven days to October 26, with data for the most recent four days (October 27-30) excluded as it is incomplete and does not reflect the true number of cases.
The rate is expressed as the number of new cases per 100,000 people.
From left to right, it reads: name of local authority; rate of new cases in the seven days to October 26; number (in brackets) of new cases recorded in the seven days to October 26; rate of new cases in the seven days to October 19; number (in brackets) of new cases recorded in the seven days to October 19.
South Staffordshire 401.1 (451), 237.5 (267)
Cannock Chase 343.4 (346), 230.2 (232)
Walsall 336.3 (960), 235.0 (671)
Sandwell 317.9 (1044), 223.5 (734)
Stoke-on-Trent 315.9 (810), 221.6 (568)
Birmingham 276.4 (3156), 240.6 (2747)
Dudley 260.6 (838), 163.9 (527)
Wolverhampton 251.0 (661), 197.8 (521)
Stafford 243.3 (334), 162.4 (223)
Lichfield 234.8 (246), 164.2 (172)
Solihull 229.2 (496), 225.5 (488)
Telford and Wrekin 219.6 (395), 168.5 (303)
Shropshire 135.5 (438), 87.3 (282)
Mr Wright said discussions would not look “at the numbers alone” but also the broader picture.
“It may well be the case we’ll be looking at the whole West Midlands combined authority area,” he added.
Any final decision on a Tier 3 move would be taken by the Government and is not expected to be announced until late next week, at the earliest.
Walsall, Wolverhampton, Sandwell, Solihull and Birmingham are all currently in Tier 2 "high risk" category, while Dudley and Staffordshire are moving from Tier 1 "medium" into Tier 2 on Saturday.
The South Staffordshire, Walsall and Cannock Chase boroughs currently have the highest rates of infection in the region.
Mr Wright said: "We expect that some of our authorities will be discussed at national bronze silver and gold in terms of potential escalation to level three, and this will take place on Monday to Wednesday next week.
"However negotiations on level three have not started and within the current framework won't begin and will depend on the formal conclusions of gold and an announcement from parliament, so the earliest that could happen is by Thursday next week."
He added: "This doesn't mean that we will end up in level three, it's not inevitable but it will become more likely if the rate of infection continues to increase."
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Councillor Ian Ward, the leader of Birmingham City Council, called for a national circuit breaker lockdown.
He said: "I would have hoped that we'd have had the opportunity to speak with the Government this week, our 14-day review of being in Tier 2 came to an end last Tuesday but unfortunately we've not had an opportunity to have a conversation with the Government this week.
"If you look at the data for Birmingham and indeed other parts of the West Midlands, I believe you have to conclude that a move to Tier 3 is inevitable at some stage.
"The problem is that the Tier system just isn't working, places in Tier 3 are still seeing a rise in cases.
"I don't believe that a move to Tier 3 is the answer, because I don't believe that it will be enough. I'm of the opinion that England needs to follow France Germany and Wales with a national circuit breaker as quickly as possible.
"We must not repeat the mistake of last March in not moving soon enough."
Andy Street, Mayor of the West Midlands, added: "The data has clearly drifted against us.
"I'm very clear that we can't stand still with our restrictions, we will need to move to further restrictions in some, if not all, parts of the conurbation. Exactly what that will mean has not yet been agreed."
Meanwhile the West Midlands Police and Crime Commissioner David Jamieson said the number of Covid-related reports have risen from 150 per day two weeks ago to 250 per day now.
He also said personally he agrees with Councillor Ward that there is now a need for a circuit breaker.