WASHINGTON — The Trump administration is considering deep cuts in the budgets of the Coast Guard, the Transportation Security Administration and the Federal Emergency Management Agency as it looks for money to ratchet up security along the southern border, according to a person familiar with the administration’s draft budget request.

The goal is to shift about $5 billion toward hiring scores of additional agents for Customs and Border Protection and Immigration and Customs Enforcement, as well as toward infrastructure to support a crackdown on illegal immigration at the border. A significant portion of the money would go toward erecting a wall along the border with Mexico, one of President Trump’s signature campaign promises.

To fund those efforts, though, the plan would seek significant reductions in other areas, including a 14 percent cut to the Coast Guard’s $9.1 billion budget and 11 percent cuts to both the T.S.A. and FEMA. The three agencies have played high-profile roles in the Department of Homeland Security’s post-Sept. 11 security architecture.

All told, the plan would increase the department’s budget by 6.4 percent, to $43.8 billion, for the 2018 fiscal year, also using savings from other executive branch departments to fund it.