Ever since Gov. Chris Christie of New Jersey killed an expensive plan for a new commuter rail tunnel to Manhattan, the Bloomberg administration has been working on an alternative: run the No. 7 subway train under the Hudson River.

The plan envisions the No. 7 stretching from 34th Street on the Far West Side of Manhattan to Secaucus, N.J., where there is a connection to New Jersey Transit trains. It would extend the New York City subway outside the city for the first time, giving New Jersey commuters direct access to Times Square, Grand Central Terminal and Queens, and to almost every line in the system.

Like the project scuttled by Mr. Christie, this proposed tunnel would expand a regional transportation system already operating at capacity and would double the number of trains traveling between the two states during peak hours. It would do so at about half the cost, an estimated $5.3 billion, according to a closely guarded, four-page memorandum circulated by the city’s Hudson Yards Development Corporation.

Unlike the old project, the new plan does not require costly condemnation proceedings or extensive tunneling in Manhattan, because the city is already building a No. 7 station at 34th Street and 11th Avenue, roughly one block from the waterfront. In July, a massive 110-ton tunnel boring machine completed drilling for the city’s $2.1 billion extension of the No. 7 line from Times Square to the new station.