NCAA executives met with the Justice Department's antitrust chief in November to discuss the association's plan to change its rules that prevent student-athletes from profiting on their names, according to people familiar with the matter.

Several officials, including the NCAA's chief lawyer, Donald Remy, met with Makan Delrahim to explain the organization's views on the issue and its thinking on changes it is considering, said the people, who declined to be named because the conversation was deemed confidential. Delrahim, assistant attorney general of the Justice Department's antitrust division, meanwhile, told the NCAA that the antitrust division is following the issue, the people added.

The meeting highlights the mounting political pressure the NCAA is facing to change a system that critics have argued is unfair or even akin to price fixing, putting it in potential violation of federal antitrust laws. State governments are threatening to force change upon the NCAA through legislation. But the specter of the DOJ bringing suit against the organization – should it wish – puts a powerful set of eyes on the NCAA as it formulates its policies.

Existing NCAA policy forbids student-athletes from making money off their name, likeness or image through opportunities like paid sponsorships. That's even as the NCAA makes money by promoting the games its athletes play, and those athletes risk injuries that put their future earning potential on the line. The nonprofit institution represents more than 1,000 schools, and takes in $1 billion a year – more than three-quarters of which comes from the Division 1 men's basketball championship television and marketing rights. Top college coaches can make millions annually.

The NCAA has acknowledged a need to modernize its policies. But it has also said it is intent on protecting student-athletes from becoming money-driven employees, rather than education-focused students. The organization does not want student-athletes to benefit from special treatment.

California in September became the first state to pass a law that overrode the NCAA, granting college athletes the right to paid endorsement deals and agents. The law goes into effect in 2023. Representatives from states including Ohio, Colorado, Florida and Illinois have indicated they will go forward with legislation aimed at targeting the NCAA's policies.

President Donald Trump has not weighed in publicly on the matter, but he is paying attention to it, a top White House aide told CNBC. Trump, a football fan, attended the College Football Playoff national championship game in New Orleans on Monday night to a standing ovation.

The executive director of the National College Players Association, Ramogi Huma, delivered a speech in September at a DOJ antitrust division workshop in which he urged the department to investigate NCAA antitrust violations.

"This NCAA price-fixing is counter to America's economic principles of free enterprise," he said.

"In addition, there is a strong civil rights concern given African Americans comprise a disproportionate percentage of players in Division I revenue-generating teams, yet suffer the lowest graduation rates."