Story highlights Puzder had some pointed words about Trump during the Republican primary.

"Sometimes he says things that concern me, not for winning the nomination, but for winning the presidency," Puzder said.

(CNN) Donald Trump's labor secretary nominee, fast-food executive Andrew Puzder, had some pointed words during the Republican primary for his potential new boss.

Before Trump became the Republican nominee, Puzder warned that outsider candidates like Trump could lead to a Republican loss in the general election by turning the party into the "bigoted, anti-woman, anti-immigrant" party. He also expressed his disapproval of Trump's rhetoric on immigration and described Trump's positions as "fringe."

Puzder, who heads CKE Restaurants, ultimately backed Trump during the 2016 general election. But appearing on the Fox Business network in October 2015 , Puzder warned what could happen to the Republican Party under an outsider candidate.

"I'm concerned because while those candidates do well in the Republican primary, I really don't care who wins the next Republican primary," Puzder said.

"I become a one issue voter. Who can win. And when you look at these outsider candidates, when the polls put them up against, national polls, put them up against Hillary Clinton or Bernie Sanders, they do not do as well as candidates like Jeb Bush or Marco Rubio, and that's a problem because we're not going to win this election if we're the bigoted, anti-woman, anti-immigrant party, and sometimes you get comments like that, that are very popular."

Read More