It will make all the difference in the world," Dr Anthony Fauci told Fox News Sunday. "He's a very widely popular person among Republicans."
A recent US opinion poll showed as many as 49% of Republican male supporters did not want to get vaccinated.
Mr Trump last month said, "everybody, go get your shot" at a conservative forum.
It was the first time he publicly encouraged Americans to do so. He has not commented on the issue since then.
Mr Trump, who was privately vaccinated in January, was absent when four other ex-presidents - Barack Obama, George W Bush, Bill Clinton and Jimmy Carter - appeared last week in a public service announcement for the vaccination.
He remains a major force in the Republican party, getting a warm reception at the Conservative Political Action Conference (CPAC) at the end of last month.
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The US is by far the world's worst-hit country by the pandemic, with more than 530,000 Covid-related deaths and nearly 29.5 million infections, according to Johns Hopkins University.
What did Dr Fauci say?
Dr Fauci, the chief medical adviser to President Joe Biden, told Fox News Sunday: "If he [Trump] came out and said 'Go and get vaccinated, it's really important for your health, the health of your family, and the health of the country, it seems absolutely inevitable that the vast majority of people who are his followers would listen to him.
"He's such a strong popular person. I cannot imagine that if he comes out that they would not get vaccinated."
Dr Fauci said the Trump administration was "very successful in getting us the vaccines we have right now".
"It seems like an intrinsic contradiction, the fact that you have a program that was started during his presidency, and he's not out telling people to get vaccinated.
"I wish he would. He has such incredible influence over people in the Republican party - it would really be a game-changer if he did," Dr Fauci said.
media caption each one of these people mattered'
The number of vaccine doses administered each day has been steadily rising in the US, and on Saturday alone about three million people got the jab - an achievement hailed by Dr Fauci.
About one in five Americans have received at least one dose, with about one in nine fully vaccinated, the Associated Press news agency is quoting as saying America's Centers for Disease Control and Prevention.
Last week, Mr Biden said in his first primetime address as president that he was hopeful America could "mark independence" from Covid-19 on 4 July if people got vaccinated.
Mr Biden previously set a target of 100 million vaccinations by his 100th day in office. But in his speech, he said this target would now be reached on day 60, which is 20 March.