Donald Trump has told the Senate’s top Democrat, Chuck Schumer, that he will unfreeze funds for major infrastructure projects in New York City if he supports renaming Dulles international airport and Penn Station after him.

The demand, which was first reported on Thursday by Punchbowl News, comes after the president in October halted $18bn in funding for a major subway line expansion in New York City as well as a new rail tunnel connecting the city to New Jersey. The funding freeze was announced on the first day of a 43-day government shutdown in which Schumer, who represents New York, played a major role.

A spokesman for Schumer did not respond to a request for comment from the Guardian.

Trump, who is not eligible to serve another term as president, has moved to emblazon his name on a host of government buildings and websites since taking office a year ago, including the Kennedy Center and the US Institute for Peace. It is unclear if either change is legal.

He also pushed congressional Republicans to create new tax-advantaged investment accounts for young people dubbed “Trump Accounts”, and announced a new government-run website to sell discounted prescription drugs called TrumpRX.com.

The president is also reportedly planning to build a 250ft arch across the river from Washington DC that would dwarf the Lincoln Memorial.