The source cautioned that the meeting has not taken place yet and "anything can happen" -- but added that the former senator's ouster is expected.
DeMint's anticipated departure, first reported by Politico
, has spurred speculation that White House chief strategist Steve Bannon
could be in line to take the job.
However, the source and another person with knowledge of the situation insisted that no one involved in the decision-making process has suggested -- or even implied -- that Bannon could replace DeMint.
Their insistence comes after Mike Needham, the CEO of Heritage Action, the foundation's political arm, refused to directly answer a question from "Fox News Sunday" host Chris Wallace about whether Bannon might replace DeMint.
Asked what he could tell Wallace, Needham responded: "That there's a lot of speculation in the room and in the media that never misses a chance to divide and attack conservatives."
Asked directly if DeMint was on the way out at Heritage, Needham said: "I don't know. There's a lot of speculation and rumor, and I'm not going to add to the speculation and rumor."
"And Steve Bannon?" Wallace asked.
"There's a lot of speculation and rumor, and I'm not going to add to the speculation and rumor," Needham responded again.
DeMint, the former South Carolina senator known for helping fund far-right conservative Republican primary challengers through his Senate Conservatives Fund, resigned from his seat in 2013 to take the helm at Heritage.
The organization has been closely linked to President Donald Trump's campaign and his White House -- including helping craft the list of potential Supreme Court nominees
that included recently confirmed Justice Neil Gorsuch
Its board includes Rebekah Mercer, the GOP financial titan who is close to Trump's organization and holds a stake in Breitbart, the right-wing news outlet that Bannon ran prior to joining Trump's campaign.
Heritage, which has advanced conservative policy measures since Ronald Reagan's presidency, was deeply involved in Trump's transition effort
More recently, though, the group bucked Trump and House Speaker Paul Ryan and opposed the GOP plan to repeal and replace Obamacare
-- instead pushing for a vote immediately to repeal the Affordable Care Act without replacement provisions in place.