“The West Side Rail Yards will showcase how sustainable construction, innovative landscape design and breathtaking architecture can form a vibrant 24-hour mixed-use community of culture, business, housing and recreation,” Jordan Barowitz, a spokesman for the Durst Organization, said.

Now, the ICP rents, at below-market rates, about 25,000 square feet in a Durst-owned building at Sixth Avenue and 43rd Street for its museum and storage, and another 40,000 square feet across the street for its school, according to its director, Willis Hartshorn. Moving to the West Side would enable the organization to consolidate into one space as large as 125,000 square feet.

"We are anticipating growth and anticipating a future and the rail yards look to us like one of the great opportunities in New York," Mr. Hartshorn said.

Bids for the rail yards are due Thursday. Having a cultural organization in hand is not necessarily going to be a huge asset in this battle, since the city has said that it would help find one willing to move out there—but it couldn’t hurt.