Senior officials at the Department of Homeland Security are floating a proposal that would require foreign students to reapply for permission to stay in the United States every year, a controversial move that would create new costs and paperwork for thousands of visa holders from China, India and other nations, according to two federal officials with direct knowledge of the discussions.

Officials caution that the plan is in the preliminary stages and would require regulatory changes that could take a minimum of 18 months. The plan may also require agreement from the State Department, which issues visas. The officials say the proposal seeks to enhance national security by more closely monitoring the students.

The discussions are emerging at a time when foreign student enrollment has reached a historic high in the United States and is injecting billions of dollars into the economy, according to the Institute of International Education (IIE), a New York nonprofit group.

It also comes as the Trump administration is working to tighten screening for foreign visitors and implement a travel ban on certain citizens from six Muslim-majority countries.

DHS spokesman David Lapan declined to comment on the specifics of the discussions Friday but confirmed that the international student program is one of many under review.

“DHS is exploring a variety of measures that would ensure that our immigration programs — including programs for international students studying in the United States — operate in a manner that promotes the national interest, enhances national security and public safety and ensures the integrity of our immigration system,” he said.

Foreign students make up 5 percent of the 20 million students attending colleges and universities across the United States. Universities are increasingly courting such students because they add diversity and boost school coffers by paying full tuition. Foreign students added more than $35 billion to the U.S. economy in 2015, according to IIE.

Some DHS officials have raised concerns that student visas are too open-ended. An estimated 2.8 percent of the more than 1.4 million student and exchange visa holders overstayed their visas last year, more than double the national average for visitors, according to a DHS report.

Though the State Department issues student visas, DHS’s Immigration and Customs Enforcement agency plays a key role in overseeing them through its Student and Exchange Visitor Program.

That program coordinates with colleges and universities so that school administrators vouch for the foreign students attending their schools. Students are charged a one-time fee of about $200 for that program, but under the changes being discussed, such fees would be charged every year, according to officials familiar with the conversations.

Officials are also considering attaching definitive end dates to students’ study programs that would require them to reapply for permission to stay in the United States if they move from one program to another, such as from undergraduate to graduate school.

Or, if foreign students do not graduate on time, they might have to apply to extend their study program.

Under current federal regulations, foreign students’ immigration status in the United States is valid as long as they are enrolled in school and follow the rules. Students can transfer from one educational institution to another and many stay in this country for years without having to reapply for permission.

Officials expect the proposal under discussion could generate stiff resistance among university officials because it could cost schools dearly.

The changes could lead to fewer foreign students coming to the United States and greater administrative costs for the schools to keep their students’ paperwork up to date, according to people familiar with the discussions.

Jill Welch, deputy executive director for public policy for NAFSA: Association of International Educators, called requiring foreign students to reapply each year for permission to be here “duplicative and unnecessary.”

“Generations of foreign policy leaders agree that international students are an asset to our nation, not a threat,” Welch said. “We urge the Department of Homeland Security to consult carefully with stakeholders like NAFSA who have worked for decades to protect our security and increase our economic prosperity before making any rash decisions that can have potentially irreversible consequences.”

Pedro Ribeiro, a spokesman for the Association of American Universities who is a former deputy assistant secretary of homeland security in the Obama administration and a former assistant ICE director, called the policy “both a policy and logistical nightmare.” The DHS and the State Department “simply don’t have enough counselor and immigration personnel to properly administer a change to the visa program like the one proposed,” Ribeiro said. “It would also have a tremendous chilling effect on students who would have to spend more time doing paperwork than studying.”

As of May, Asian students accounted for 77 percent of international students this year, according to a recent ICE report.

China has 362,368 students in the United States this year, the most of any country, according to ICE. India, which has one of the fastest-growing populations of citizens on student visas in the United States, has 206,698.

South Korea ranks third (71,204 students), and Saudi Arabia is fourth, though its enrollment dropped 19 percent this year to 55,806 students.

California has the highest number of foreign students, more than 200,000, followed by New York and Texas, according to ICE. Other states with significant numbers include Massachusetts and Illinois. New York University has the largest number of foreign students, followed by the University of Southern California.

In Maryland, foreign student enrollment rose 10 percent among bachelor’s-degree candidates this year.

Nearly half of foreign students — and 84 percent of those from India — are studying science, technology engineering or mathematics.

Susan Svrluga contributed to this report.