Pfizer has said it expects to report required safety data next week and can then apply for an emergency use authorisation.
Mr Trump's remarks came after he received an update on 'Operation Warp Speed,' an administration effort to turbocharge development of a vaccine.
Criticism of the administration's response to the virus, which has killed more than 235,000 Americans, became a rallying cry for Democrats ahead of the 3 November election.
Mr Trump also appeared to acknowledge for the first time the possibility of an upcoming Biden administration, though he stopped short of conceding the race and did not mention his Democratic rival by name.
Since the election, Mr Trump has persisted with unfounded accusations of widespread voting fraud. But while he has continued to make such claims on Twitter, he did not repeat them in his public remarks on Friday.
The last time Mr Trump spoke - in the White House briefing room two days after the election - he said without evidence that if "legal" votes were counted he would "easily win" the election.
Mr Biden solidified his victory over Mr Trump on Friday after the state of Georgia went his way, leaving Mr Trump little hope of reversing the outcome through legal challenges and recounts.
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