"Donald Trump's the only person that can do that right now," the West Virginia Democrat told CNN in an interview following a job fair hosted by his office.
Manchin said he's spoken about the issue with Trump "in passing" but that they haven't had a deep conversation about it.
The New York Times Magazine reported that Trump called Manchin in December
shortly after Manchin was on MSNBC's "Morning Joe," talking about the fourth anniversary of the Newtown Elementary School massacre
. Manchin did not give details about the call but said he sensed "a complete opportunity" for new gun-safety legislation, according to the magazine.
A few months after Newtown, Manchin teamed up with Republican Sen. Pat Toomey of Pennsylvania to propose legislation expanding background checks on gun sales, including private transactions.
The compromise amendment failed to get enough votes to advance in the Senate.
Manchin, a gun owner, made news at the time for sponsoring the amendment, given his state's strong Second Amendment culture. The National Rifle Association quickly attacked Manchin with TV ads, and it's an issue that could come up in his re-election bid next year.
Asked Friday if he thinks the background check proposal will reemerge under a new president, Manchin said he thinks Trump can apply some "gun sense" to the measure. "I truly believe he can make a difference."
He argued that many of his constituents said four years ago they were fine with the substance of the amendment but feared it would lead to a slippery slope for Obama to implement more gun control.
People have different perceptions of Trump, he added.
"There's no one who believes he's going to take their guns away," Manchin said.
Manchin said Trump could do this by saying he wants to keep guns out of the hands of terrorists and criminals. "He would be the person that could help us with that," he said.
"There's a reason that certain people shouldn't be able to have access to guns. Every law-abiding gun owner understands that," he said. "They read our bill and saw we had a good piece of legislation, but no one had the fortitude to do it. And he could do it."
Asked if he thinks the legislation could come back in the next couple of years, Manchin said, "we'll see."
"He could if he wants to," he said.
So far as President, Trump has signed one gun-related law
, which repealed an Obama-era regulation aimed at keeping guns out of the hands of some severely mentally ill people.