President-elect Donald J. Trump’s transition team has asked federal border protection officials for guidance on where a new wall separating the United States from Mexico — a signature promise of Mr. Trump’s campaign — can be erected, according to a Democratic congressman from Texas who opposes the idea.

But the officials exploring possible paths for such a barrier also appear to be considering fencing and other options short of the “big, beautiful wall” that Mr. Trump regularly vowed to erect, at Mexico’s expense, along a border of more than 1,900 miles.

The discussions with federal border officials, along with separate talks with city officials in Laredo, Tex., one of the busiest crossings, come as aides to Mr. Trump maintain that construction of a border wall will be a top priority of his administration.

In an interview, Representative Henry Cuellar, whose district includes a 200-mile stretch of border and reaches 150 miles north, to San Antonio, said that the chief patrol agents from two border sectors in the state had contacted him last week. They said they were doing so at the request of the incoming administration, Mr. Cuellar said, and solicited his ideas for where such a wall, or a fence, should be built.