By Veronica Stracqualursi, Annie Grayer, Alayna Treene, CNN

(CNN) — House Speaker Mike Johnson on Tuesday said he has spoken with Donald Trump about the possibility of the president seeking a third-term but that he sees no path for it as any change to the US Constitution would be well after Trump has left office.

“Well, there’s the 22nd Amendment,” Johnson, who is a constitutional lawyer, said in response to a question about his comfort-level with the president floating a 2028 bid.

“It’s been a great run. But I think the president knows, and he and I have talked about, the constrictions of the Constitution, as much as so many of the American people lament that,” he said.

The president, he said, is trolling members of the other party when he talks publicly about the topic.

“The Trump 2028 cap is one of the most popular that’s ever been produced. And he has a good time with that, trolling the Democrats, whose hair is on fire about the very prospect,” he told reporters on Capitol Hill.

The Republican leader’s acknowledgment that he and Trump have discussed issues surrounding a third-term adds credence to warnings from the president’s opponents that he is seriously flirting with upending the Constitution. But Johnson’s quickly throwing cold water on the suggestion underscores how little support Trump would have if he actually tried to move forward with it.

Johnson said he had spoken with Trump Tuesday morning while the president is overseas in Japan, but he did not specify when the pair had discussed the Constitution.

Amending the Constitution, he noted, would be a lengthy and arduous process, saying, “I don’t see a way to amend the Constitution, because it takes about 10 years to do that, as you all know, to allow all the states to ratify … what two-thirds of the House, three-fourth of the states would approve. So I don’t, I don’t see the path for that.”

Trump on Monday continued to entertain the idea of running for a third term, telling reporters that he’d “love to do it,” while also floating the possibility of a Vice President JD Vance and Secretary of State Marco Rubio pairing in 2028. But he did rule out one proposed end-run around the Constitution, saying it would be “too cute” for him to run as vice president in order to later ascend back into the White House after the elected president resigned.

“I think the people wouldn’t like that because it’s too cute. It’s not — it wouldn’t be right,” he said, although he tried to reserve the legal right to do it.

At the White House, Trump has joked about running for a third term and Trump 2028 hats are on display in a room near the Oval Office. Recently, Trump posted images of the ’28 hats on the Resolute Desk when the House and Senate minority leaders, Hakeem Jeffries and Chuck Schumer, came to the Oval Office. But some people close to the president say that inside the administration, a third term is not viewed as something he is seriously considering or planning to do.

The idea of running for a third term is “like catnip” for the media and Democrats, Trump’s allies argue, ginning up the type of attention the president enjoys, one source said.

That attention intensified last week when The Economist published an interview with Steve Bannon, a MAGA influencer and former Trump adviser, who claimed “there is a plan” for Trump to run for a third term. Bannon is notably far less close to the president and his team than he was during Trump’s first term, and some White House officials viewed his comments as an attempt to draw attention to himself. But the seemingly outlandish ideas of Trump and people in his orbit sometimes find their way to reality.

The sources insisted Trump isn’t actually plotting a 2028 campaign. That is not only because it would take a Constitutional amendment to make it legal, but the president is also aware of his age and cares deeply about his legacy. People close to him argue he never wants to be viewed like former President Joe Biden, whose age and health became a fixture of his presidency. If Trump were to take office again for a third term, he would be 82 years old.

“He said publicly he’s not gonna do a third term. Anytime it comes up, it’s Trump being Trump. He’s going to do the ‘Many people would love that!’ thing,” a person close to Trump said.

They also argued the president doesn’t like to point out that he only has three years left, trying to swat away any talk of him being a lame duck president.

The person close to the president argued that not only is Trump “not seriously thinking about 2028, no one is seriously thinking about it right now,” including people that Trump has hinted could succeed him, like Vance and Rubio.

“That’s something we all expect to play more of a role come the midterms,” they said.

This story has been updated with additional reporting.

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CNN’s Kit Maher and Zachary B. Wolf contributed to this report.