All inpatients at Weston General Hospital will undergo another test for coronavirus this week.
The hospital, in Weston-super-Mare, stopped accepting new patients, including in A&E, on 25 May due to a high number of Covid-19 cases.
Tests last week showed no new inpatient cases and another round of testing will begin imminently.
The majority of the 1,700 staff have now been tested with about 6% testing positive but showing no symptoms.
Managers at the University Hospitals Bristol and Weston NHS Foundation Trust say if the new round of testing shows no new cases, this would indicate there was “no in-hospital transmission” of the infection.
In the meantime, about 100 staff who are infected have been told to self-isolate and arrangements have been made for new patients to be treated elsewhere.
Medical Director Dr William Oldfield said signs were “encouraging” after the first round of tests.
“The results from our inpatient testing have identified no new cases of Covid-19, which suggests the actions we have taken to control the situation are working.
“We will retest all our inpatients again. We will also repeat testing of all staff. The results from this will indicate whether the staff working in the hospital are remaining free of infection.
“We are continuing to safely discharge patients as appropriate when they no longer need our care, and as patients are discharged areas are being deep cleaned to get the hospital ready to reopen.”
The trust would not say when the results of the second round of testing would be released.