NHS bosses in Dudley said they were concerned by potential 'false negatives' and had carried out repeat tests where medics believed the person did in fact have Covid.
Diane Wake, chief executive of the Dudley Group NHS Trust, which runs Russells Hall Hospital, said patients had presented with clear symptoms of coronavirus but gone on to receive negative tests.
Swab tests are only thought to be 70 per cent accurate and it is understood there have been cases of possible 'false negatives' across the region.
Ms Wake said patients who have symptoms are treated as if they have Covid, even if the test comes back as negative. However, they are not counted among coronavirus patients unless there is a positive test.
She told a board meeting: "What we're seeing is that even though we may suspect they have Covid they are coming back as negative. We are doing a number of repeated tests where it's highly suggestive we are treating Covid.
"We're making sure we're not having a spread. Where we think there is a chance they have Covid we are maintaining isolation or specific areas in the organisation as a matter of caution."
Ms Wake told the Express & Star following the meeting: "It is believed the Covid swab test is about 70 per cent accurate. This is the same test that is used for both staff and patients.
"When there is strong clinical indication that what they are dealing with is clinically Covid then they will treat patients as if they have it e.g. in a side room, appropriate treatment, etc.
"However, they are not counted in our numbers unless a positive test result comes back. This is what is advised in the national guidance for clinicians."
Elsewhere, other hospital trusts have said they were not aware of "significant issues" regarding false negatives in their area, but knew it was a possibility.
A spokesman for Walsall Public Health said: "The Covid test is very sensitive and specific and there is always the possibility of a small number of false returns and this is factored into testing practices and consequent actions. We are not aware of significant issues with false negative tests in Walsall."
Michelle Rhodes, chief nurse at the University Hospitals North Midlands NHS Trust, which runs Stafford County Hospital, added: “Testing plays an important role in quickly identifying and responding to any positive cases that present in our hospitals.
"While most people can produce the virus early, sometimes if the test is taken just before a patient shows symptoms and we don’t get high rates of virus, or they are only producing it from their lungs and we don’t see it in their nose and throat it can affect the result of the test.
"For those patients displaying symptoms that are very convincing and are clearly unwell, our clinicians will keep the patient isolated and retest."