Heitkamp told CNN Thursday she has no inkling of what the meeting may be about, but said she was open to discussing serving in a Trump administration.
News of the meeting set off a panic among top Democrats, some of whom began to privately make the case that Heitkamp should stay in the Senate rather than give up a seat that would likely be a GOP pickup. The incoming chairman of the Senate Democrats' campaign committee told CNN he had spoken with Heitkamp about the issue Thursday.
A transition source said Heitkamp could be a possibility for energy secretary.
"I think it's absolutely critical to have a conversation," Heitkamp said when asked if she would be open to being in the Trump administration. "It's good for my state. It's good for the work that I do here, to understand and share some priorities for the country and for the state of North Dakota and I look forward to having that discussion."
In a statement about the meeting, Heitkamp said she would work with both sides of the aisle -- whatever her role.
"Whatever job I do, I hope to work with the President-elect and all of my colleagues in Congress on both sides of the aisle to best support my state," she said.
While any position is far from a done deal, having Heitkamp in the Cabinet would be a double win for Republicans, and a blow to Democrats.
Heitkamp comes from a heavily red state, and is one of the more vulnerable senators up for re-election in 2018. But defeating an incumbent is usually a tricky proposition, meaning an open seat in North Dakota would give Republicans a much better chance of adding to their majority in the Senate.
"Obviously incumbents have an advantage over challengers," said Sen. Cory Gardner of Colorado, who will chair the National Republican Senatorial Committee next year, when asked about the Heitkamp news.
New York Sen. Chuck Schumer, the incoming Senate minority leader, could have the most to lose if Heitkamp left the chamber. Asked if he had any concerns, Schumer said: "No comment."
Senior aides said Thursday the pressure campaign would intensify if a possible Trump appointment looked real.
Rep. Chris Van Hollen, the soon-to-be Maryland senator who will chair the Democratic Senatorial Campaign Committee in the next cycle, told CNN he spoke to Heitkamp about the matter.
"I told her exactly that: I'm sure she'll do what's right for the people of North Dakota," Van Hollen said.
The appointment would also give the Trump administration a token opposition member -- a conventional move for presidents.
If she were to leave the Senate, it would immediately give Democrats one less member in the minority. Though they would be in the minority regardless, the balance of power is expected to be 52-48 after the Louisiana Senate runoff election, and every vote lost would make it harder for Democrats to peel off Republicans to oppose Trump's policies.
Though North Dakota is one of a handful of states that does not allow the governor to appoint a successor, a special election would heavily favor Republicans, as the state is strongly Republican and Democrats do not have a deep bench of politicians in the state.
Her departure would also be a further blow to Democrats' hopes of retaking the majority in 2018 -- already a long shot. Democrats will have to defend multiple red state seats in 2018 and Republicans have very few vulnerable senators up for re-election that year.