The boss of the trust which runs Russells Hall said the number of Covid patients had "gone down significantly" since the start of the year.
On Thursday, there were four patients in hospital, including one in intensive care. There was one death in the 24 hours to Thursday.
Cases have begun to rise again nationally following the easing of lockdown measures, sparking debate about whether Boris Johnson should proceed with 'freedom day' as planned on June 21.
But there has been no indication yet of a significant rise in hospital admissions or deaths, suggesting the vaccination programme is having the desired impact.
Trust chief executive Diane Wake said the hospital was preparing for the prospect of a surge in patients over the coming weeks.
She also confirmed staff were set to receive booster vaccinations from September.
Ms Wake said the trust was unable to provide details of whether the patients currently in hospital had been vaccinated.
She told the trust board: "The number of (Covid) admissions have gone down significantly.
"We are getting one or two patients on a daily basis. That is a massive improvement on where we were at the height of Covid-19. Lengths of stay have gone down massively as well.
"We are seeing community transmission of 25 per 100,000 of the population. The biggest pressure around community transmission is Birmingham where it is 54 per 100,000 and Walsall at 45 per 100,000 so vigilance is really important."
She added: "We are preparing for a surge in Covid patients. We are also proposing in September to deliver booster vaccinations to our staff in conjunction with flu."
Ms Wake said it was crucial that under-25s take up the vaccine in order to slow the spread of the virus.
"It is important to encourage as many possible to have the vaccine," she said.