The comments came during a programme at the Lincoln Memorial in Washington. He said that several pharmaceutical companies are close to developing the vaccine.
Donald Trump said he is not concerned about which country develops a vaccine first but just want to get a vaccine that works.
Public health officials have said a coronavirus vaccine could take a year to 18 months. Vaccines often take many years to develop and distribute.
There are 14 potential vaccines for COVID-19 under development as part of the effort to fast-track vaccine development.