NHS Blood and Transplant has issued the appeal.
Scientists need to help make sure there is enough plasma for clinical trials and to treat patients.
The blood plasma from people who've recovered from the virus could save the lives of people who are still ill, according to NHS Blood and Transplant.
That's because it contains antibodies against the virus which can be transfused into people who're struggling to develop their own immune response.
More than 650 donations of COVID-19 convalescent plasma have already been taken at Oxford donor centre, but more Is needed from those who've had a positive test.
Professor Dave Roberts, Associate Director for Blood Donation at NHS Blood and Transplant, said: "Every new offer to donate is incredibly valuable. We particularly need men to come forwards as they generally have higher antibody levels.
"We need to collect convalescent plasma now, to make sure plasma is readily available for the trial to treat people currently in hospital.
"Donations can also be frozen to ensure convalescent plasma is readily available, should there be a rise in infections in the coming weeks.
"Please, help the NHS fight COVID-19 by donating at Oxford donor centre. You could save lives."