Professor David Loughton CBE, chief executive of Wolverhampton's NHS Trust, which runs News Cross Hospital, made the comments during a regional media briefing on Covid.
Asked when people will begin to be vaccinated at the Dudley attraction, he said: "As far as the Black Country Living Museum is concerned, its opening is fairly imminent. I believe it is about [January] 25. We are in the final stages of identifying a number of other sites. We will roll those out as quickly as possible."
It was revealed at the start of December that the museum on Tipton Road, which has been forced to close under the national lockdown, had been earmarked as a potential vaccination site along with Millennium Point in Birmingham which opened last week.
Mr Loughton also expressed his frustration about people denying Covid's threat and issued a stark warning to those not taking the pandemic seriously.
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New Cross Hospital expanded its intensive care capacity to double its usual level this week, while Wolverhampton currently has the highest Covid infection rate in the West Midlands with 997.1 cases per 100,000 people.
Mr Loughton said: "I have got several empty wards and the reason for that is because they were for elective surgery. Those staff have been redeployed to more critical areas to deal with Covid patients. That is why I have got empty wards. To say the NHS is making this [Covid] up is completely untrue and we have got to continue working with what we have got.
"I don't expect, and I don't think it is going to be an exact science, that it will be about January 27 when we hit the peak.
"The NHS has got to deal with these patients. There is enormous stress on staff because they have now had 10 months dealing with this.
"Yes, we got some respite in the summer, but it has started to ramp up. We have seen the numbers now are higher now.
"Our peak day was on April 10 and we have surpassed that number now. It is a difficult situation to deal with.
"The most difficult thing for staff in the NHS is, nobody went to medical school, or nurse training, to watch people die.
"That wasn't what they were trained for. I have got some problems with two intensive care consultants because they wake up at 4am in the morning, and remember the faces of the people who they told 'I am going to put you to sleep now, you may never wake up'.
"That is not easy for the staff in the NHS to deal with. You come into my organisation, one in four people will not walk out.
"The number is coming down to about 21 per cent mortality. This is real, and I cannot overemphasise the need, when people are offered the vaccine, take the vaccine.
"This is absolutely real. I do not normally do social media, but some of the things that have been brought to my attention are shocking."
Staff have also been redeployed at Russells Hall Hospital in Dudley, which had 200 coronavirus inpatients this week and triple the usual number of people in critical care.