The Trump administration has sought to pressure Senator Chuck Schumer, Democrat of New York and the minority leader, to help name New York’s Penn Station and Washington Dulles International Airport after President Trump in exchange for releasing billions of dollars he has frozen for a rail tunnel under the Hudson River.

Top administration officials have told Mr. Schumer in recent weeks that the money would be released if he agreed to name the facilities in Mr. Trump’s honor, according to four people familiar with the private conversations. The people spoke on the condition of anonymity because they were not authorized to reveal the private discussions.

The push to rename the station and the airport for Mr. Trump comes as the president, who recently put his name on the Kennedy Center for the Performing Arts in Washington, has been on a renaming spree and has appeared increasingly preoccupied with his legacy.

The Trump administration began withholding funds for the new tunnel connecting New York City and New Jersey, a $16 billion project, in October. The agency overseeing its construction moved to halt ongoing work on Friday as money was running out.

Mr. Trump and Mr. Schumer met at the White House last month to discuss the frozen funds.

Though he is the top Senate Democrat, Mr. Schumer has no direct oversight over either transportation hub and rebuffed the request, according to two of the people.

The White House and the Department of Transportation did not immediately respond to a request for comment. The conversations were first reported by Punchbowl News.