The US has already started a major project to study this, involving more than 1,500 hospitals.
When a person has Covid-19, their immune system responds by creating antibodies, which attack the virus.
Over time these build up and can be found in the plasma, the liquid portion of the blood.
NHSBT is now approaching patients who have recovered from Covid-19 to see if plasma from them can be given to people who are currently ill with the virus.
A statement from the organisation said: “We envisage that this will be initially used in trials as a possible treatment for Covid-19.”If fully approved, the trials will investigate whether convalescent plasma transfusions could improve a Covid-19 patient’s speed of recovery and chances of survival.
“All clinical trials have to follow a rigorous approval process to protect patients and to ensure robust results are generated. We are working closely with the government and all relevant bodies to move through the approvals process as quickly as possible.”