It's unclear how he intends to close the entire US-Mexico border and he already earlier this year called up some military units to do border security.
On Thursday, Trump said he prioritizes border security over even the recently struck trade deal to replace NAFTA, the United States-Mexico-Canada Agreement, or USMCA.
Take, for example, the latest migrant caravan now making its way to the United States.
The remark came during Thursday's broadcast of The Five, where Kennedy, known primarily for her self-titled program on the network, sat as a panelist for a discussion on immigrants during which she argued the government hasn't implemented sufficient border control.
As a matter both USA and worldwide law, asylum is only available to those fleeing persecution on account of race, religion, nationality, political opinion or membership in a particular social group.
Mr Trump's recent comments are probably an effort to bolster support among his base by cracking down on migration.
Trump ran for president in 2016 on promises to toughen USA immigration policies and build a wall along the US border with Mexico.
"Republicans must make the horrendous, weak and outdated immigration laws, and the Border, a part of the Midterms!" he continued.
"They're saying all the right things now, and they're behaving more responsibly than they did in the spring when the earlier caravan came through and they actually issued them transit visas to continue to the United States", she explained.
The caravan has snowballed since about 160 migrants departed Friday from the Honduran city of San Pedro Sula, with many people joining spontaneously while carrying just a few belongings.
Mexican Foreign Secretary Luis Videgaray went to New York Thursday to make his request personally for the U.N. High Commissioner for Refugees to get involved.
Exhausted after tramping in the sun and rain, an advance group of the Honduran migrants on Wednesday took refuge in a church-sponsored shelter in the center of Guatemala City. "We are certainly looking for concrete results and for solutions that work for both countries".
"Just today, the Mexican government, and this is a very important step, requested the intervention of the United Nations, the Office of the High Commissioner on Refugees, to help Mexico review any asylum claims from the members of the caravan", Gutierrez said.
Arpaio applauded Trump's warning of possible financial penalties for Central American nations if the threats to the USA border are not addressed.
Guatemalan President Jimmy Morales on Wednesday dismissed threatened curbs to foreign aid, and said he had spoken with Honduran President Juan Orlando Hernandez about ensuring the migrants who want to return home can do so safely.