(U.S. Senator Joe Lieberman of Connecticut pauses during his remarks at a news conference in Stamford, Connecticut January 19, 2011.REUTERS/Mike Segar)

Former Sen. Joe Lieberman doesn't think President Donald Trump is going to have much luck getting Mexico to pay for the wall he wants built on the southern border of the US.

The former chairman of the Senate Homeland Security Committee called Trump's strategy for funding the wall "risky."

"Will Mexico pay for the wall? Not voluntarily under any means that I can see," Lieberman told Business Insider this week.

He explained why Trump's plan is dicey: "I suppose it's possible that the president and the administration would try to increase tariffs on Mexican goods coming into the United States and then use some of those tariffs to pay for the construction of the wall, but that's risky because it could lead to tariffs on the other side by Mexico for goods coming in from the United States and you know Mexico and Canada are our two biggest trading partners in the world."

Republicans have estimated the wall would cost between $12 billion and $15 billion.

White House press secretary Sean Spicer told reporters on Thursday that the administration is pushing for a 20% border tax on Mexican imports to help pay for the wall.

"When you look at the plan that's taking shape now, using comprehensive tax reform as a means to tax imports from countries that we have a trade deficit from, like Mexico," Spicer said.

Over 80% of Mexican exports went to the US in 2015, and the US imported $295 billion worth of goods from Mexico, accounting for 13.2% of all US imports.

Lieberman also said Trump's plan is too vague.

"President Trump is keeping his promises with executive orders that state an intention to do something, and that's the case here, but they're not all very detailed," Lieberman said. "He's saying 'I made this promise, I'm going to keep it, I'm going to put up a wall between Mexico and the United States, [Homeland Security Secretary] John Kelly, take care of it.' And we'll see what happens."

Lieberman also noted that the flow of undocumented immigrants into the US already seems to have diminished in recent years. And ultimately, hurting the Mexican economy could end up leading to more illegal immigration.

"The inflow of immigrants from Mexico has diminished insofar as we can count," Lieberman said. "Obviously, if somebody comes in here illegally, you don't know they're here … but we tend to count by the illegal immigrants we pick up on the way in and it's gone down mostly because the economy of Mexico has gotten better and fewer people are coming over here for income."