Dr Anthony Fauci predicted such knowledge could arrive by the end of next month or beginning of December, but warned there would not be enough doses to vaccinate everyone before 2021.
His comments come amid reports plans are being made for frontline NHS staff to receive a Covid-19 vaccine within weeks.
The Mail on Sunday said it had seen a staff memo sent earlier this month by Glen Burley, chief executive of George Eliot Hospital NHS Trust in Warwickshire, explaining that health service organisations had been told "to be prepared to start a Covid-19 staff vaccine programme in early December".
The newspaper reported the memo said: "The latest intelligence states a coronavirus vaccine should be available this year with NHS staff prioritised prior to Christmas."
Mr Burley said the vaccine was "expected to be given in two doses, 28 days apart", the Mail on Sunday said.
Appearing on the BBC's Andrew Marr Show, Dr Fauci was asked if US president Donald Trump's claims that a Covid-19 vaccine, while not a guarantee, will be coming by the end of the year were true.
Dr Fauci replied: "We will know whether a vaccine is safe and effective by the end of November, the beginning of December.
"The question is, once you have a safe and effective vaccine, or more than one, how can you get it to the people who need it as quickly as possible?
"The amount of doses that will be available in December will not certainly be enough to vaccinate everybody, you'll have to wait several months into 2021."
He said healthcare workers would likely be prioritised first for any vaccine, as well as people considered at increased risk of complications.
Dr Fauci said: "That could start by the end of this year, the beginning of January, February, March of next year.
"When you talk about vaccinating a substantial proportion of the population, so that you can have a significant impact on the dynamics of the outbreak, that very likely will not be in to the second or third quarter."
Dr Fauci expressed concern that "anti-science" sentiment could have an effect on vaccine uptake.
He told the Andrew Marr Show: "One of the things I'm concerned about in the United States is that part of the anti science translates maybe into anti vaccine."
He added: "It would really be a shame if we have a safe and effective vaccine, but a substantial proportion of the people do not want to take the vaccine because they don't trust authority."That would really be unfortunate if that's the case."
Dr Fauci said a potential coronavirus vaccine, alongside public health measures, could help move the US towards "some form of normality" next year.
He said: "I think when we get a vaccine, and we start getting people vaccinated ... over a period of several months into 2021, we will begin to approach some form of normality, depending upon how many people, what proportion of the people, take the vaccine.
"That should be combined with some degree of public health measures.”