DAVOS, Switzerland:  US Robert Mueller, Director of the Federal Bureau of Investigation (FBI) attends the session "Security is an Always-on World" at the World Economic Forum in Davos 26 January 2006.Tthe World Economic Forum this year is gathering more than 2,300 leaders, officials and executives for five days of high-powered networking.  AFP PHOTO PIERRE VERDY  (Photo credit should read PIERRE VERDY/AFP/Getty Images)

NEW YORK, NY - NOVEMBER 03:  Donald Trump attends a press conference for the release of his new book "Crippled America" at Trump Tower on November 3, 2015 in New York City.  (Photo by Noam Galai/WireImage)
PHOTO: Getty Images
DAVOS, Switzerland: US Robert Mueller, Director of the Federal Bureau of Investigation (FBI) attends the session "Security is an Always-on World" at the World Economic Forum in Davos 26 January 2006.Tthe World Economic Forum this year is gathering more than 2,300 leaders, officials and executives for five days of high-powered networking. AFP PHOTO PIERRE VERDY (Photo credit should read PIERRE VERDY/AFP/Getty Images) NEW YORK, NY - NOVEMBER 03: Donald Trump attends a press conference for the release of his new book "Crippled America" at Trump Tower on November 3, 2015 in New York City. (Photo by Noam Galai/WireImage)
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(CNN) —  

Special Counsel Robert Mueller’s team has approached the White House about interviewing staffers who were aboard Air Force One when the initial misleading statement about Donald Trump Jr.’s meeting with a Russian lawyer at Trump Tower was crafted, three sources familiar with the conversations said.

The special counsel’s discussions with the White House are the latest indication that Mueller’s investigators are interested in the response to the Trump Tower meeting. Mueller wants to know how the statement aboard Air Force One was put together, whether information was intentionally left out and who was involved, two of the sources said.

Mueller’s questions could go to the issue of intent and possible efforts to conceal information during an obstruction of justice investigation. The answers to Mueller’s questions also could illuminate the level of anxiety surrounding the meeting and the decision-making that followed.

The interviews with White House staffers who were aboard Air Force One have not begun, the sources said. They currently involve only a small number of people, but the sources cautioned that number could increase. At this time, Mueller has not asked to interview President Trump. Trump Jr. was on the Hill Thursday for an interview with the Senate Judiciary Committee.

In his first response to a report this summer about his meeting at Trump Tower, the President’s son claimed in a statement that he “primarily discussed a program about the adoption of Russian children” during his meeting with a Russian lawyer he believed to be connected to the Russian government. That claim was later debunked by multiple accounts of the meeting.

Emails later released by Trump Jr. revealed that he believed the lawyer would provide him with incriminating information about his father’s campaign rival, former Secretary of State Hillary Clinton, on behalf of the Russian government. The Trump Tower meeting also included Trump’s son-in-law Jared Kushner and then-campaign chairman Paul Manafort.

“Out of respect for the special counsel process, the White House doesn’t comment on any individual special counsel request,” White House special counsel Ty Cobb told CNN.

Mueller’s office declined to comment for this story.

Sources previously told CNN that Trump was involved in the crafting of the statement aboard Air Force One and that he involved some of his closest aides.

White House press secretary Sarah Sanders – then the deputy press secretary – confirmed in August that Trump “weighed in as any father would” during the drafting of the statement but declined to characterize his involvement further.

Mueller considers some of the aides aboard Air Force One who helped craft the statement to be witnesses.

The White House is trying to figure out legal defense funding for some of the staffers who have needed to hire lawyers as a result of the Russia probe, two of the sources told CNN.

CNN previously reported that Mueller sent a notice asking that White House staff save “any subjects discussed in the course of the June 2016 meeting” and also “any decisions made regarding the recent disclosures about the June 2016 meeting,” according to a source, who read portions of the letter to CNN.

The conversations aboard Air Force One about how to respond to reports of Trump Jr.’s meeting with a Russian lawyer may have exposed those White House aides to the special counsel’s scrutiny.

Some of the President’s closest aides who had joined Trump for the return flight from diplomatic summits in Europe, helped strategize Trump Jr.’s response to the statement, people briefed on the matter told CNN in July.

CNN’s Dana Bash contributed to this report.