President Trump's new chief of staff, John Kelly, is eyeing his Homeland Security spokesperson David Lapan for the role of White House communications director, two high-level administration sources told CNNMoney.

Lapan, who has worked with Kelly for over a decade, is at the top of a short list to serve as the White House's top official on messaging and communications. He would take the position formerly held by Anthony Scaramucci.

Kelly's interest in Lapan suggests that he is as eager to impose discipline on the White House messaging strategy as he is to impose order on the chaotic and fractious West Wing. Lapan has a background that, like Kelly's, is steeped in years of military experience. Before DHS, he led press operations at the Defense Department and the Marine Corps.

Reached for comment, Lapan told CNNMoney he had not spoken to Kelly or anyone else at the White House about the position.

"I've seen speculation, but at this point it's only speculation. I haven't talked to him or to anybody else about it," he said.

When asked if he would accept the position if it were offered, Lapan said he would have to consider it.

"Obviously I've known [Kelly] for a long time," Lapan said. "I would take seriously anything he asked. But I would also have to understand more about what it would be and all of those things. So I couldn't say today what my answer would be."

Even for a military man, the post would be a tall order. The Trump administration has been lacking message discipline since its inception, and the big question for both Kelly and his communications director will be whether or not they can rein in their ultimate boss, President Trump.

"The first question is, can this president operate under any form of traditional communications regime, and I think the answer is no," said Rory Cooper, a Republican communications operative and managing director at Purple Strategies. "I think Kelly can perhaps instill some discipline but only at the staff level, which means you still have a wild card at the top. I don't know how you plan around that from a comms perspective."

Dan Pfeiffer, who served as President Obama's senior adviser for strategy and communications, said the White House needed someone "with actual relevant experience working on the Hill or in the executive branch [who] knows how to develop and execute a strategic communications plan."

"They need to internalize the lesson that being good on Fox News is not the same thing as having a clue how to do the most basic communications work," Pfeiffer said.

Kelly has already sought to distance the administration from relying on Fox News for communications help. Before Scaramucci's exit, senior officials had been talking to former Fox News executive Bill Shine about a role with the communications team. White House sources told CNNMoney that since Kelly came on board, Shine is no longer under consideration.

Still, the White House may not have completely given up the idea of bringing in someone from Fox News. For months, the administration has been courting conservative pundit Laura Ingraham about a role with the media team. The White House sources said her name was still on the list for the communications director position. (Sources familiar with those discussions previously told CNNMoney that Ingraham would only be interested in that role if she could run communications strategy.)

The White House did not respond to repeated requests for an interview.