Ministers want to bring in the same measures that were launched this week in the North East, making it illegal for different households to mix in indoor settings – including pubs and restaurants – and in private homes or gardens.
People face fines of up to £6,400 if they breach the restrictions.
The move will affect the four Black Country council areas as well as Birmingham, Coventry and Solihull.
It is understood to be widely opposed by political leaders across the region, who fear the added restrictions are "too much, too soon" and could cause further harm to the struggling hospitality sector.
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Local politicians believe the virus is mainly spread inside homes and are hopeful that ministers will hold off on the introduction of new measures.
Extra restrictions were recommended for the region at a meeting on Tuesday under the Government's new disease containment framework, with Health Secretary Matt Hancock set to hear evidence at a meeting today before a formal announcement is made on Friday.
It is understood that West Midlands Mayor Andy Street has spoken with Mr Hancock to raise concerns over the measures.
Councillor Ian Brookfield, the leader of Wolverhampton Council, said: "There is a move now for the whole West Midlands to have the type of stringent restrictions that the North East has.
"I have been speaking to leaders across the West Midlands and everyone is saying 'this is not on'. Any measures that come in should be evidence based, and our evidence is that 90 per cent of the virus in Wolverhampton is spread through people going into other people's homes.
"We've only just had new restrictions in Wolverhampton, and we believe we should be given a chance to see if they work.
"If they don't, then we may well need something stronger in a week or two, but at the moment this is too much too soon. It is absolutely not the right move."
Councillor Wendy Thompson, Wolverhampton Council's opposition Tory leader, said: "This is immensely disappointing. It is so important for our hospitality industry, which is already under pressure, that they can keep going, and this certainly won't help."
Wolverhampton, Sandwell, Birmingham and Solihull have all had seen extra restrictions brought in during recent weeks due to rising cases.
In the seven days up to September 28, there were 146 confirmed Covid cases in Wolverhampton, a rate of 55.7 per 100,000 people.
It had hit 70.2 per 100,000 in the seven days up to September 27.
In Walsall the rate over the same period was 56.8 per 100,000, while it was 108.8 in Birmingham, 85.2 in Sandwell and 44.3 in Dudley.
Newcastle currently has the highest rate in the country at 247.5.
The new measures would also see people advised to only use public transport for essential trips. All restrictions are reviewed each week.