Sen. Mike Lee, R-Utah, said Thursday he believes a plan to require the Mexican government to hold Central Americans who forego applying for asylum in Mexico and insist on instead applying in the U.S. stands a solid chance of being adopted by both nations.

Lee, who visited Mexico earlier this month to talk with leaders there about caravans of migrants traveling to the U.S., said Mexican officials conveyed to him during his recent trip south of the border they don’t want Mexico to be “just a thoroughfare for people passing through.”