Bannon made the comments yesterday at a Manchester fundraiser for the conservative group 603 Alliance.
Democrat Hillary Clinton won New Hampshire and all four of the state's electoral votes.
Trump has cited New Hampshire as part of his unsubstantiated claims that millions of people voted illegally in 2016. He created the Presidential Advisory Commission on Election Integrity in May to investigate those claims.
Bannon says his claims are supported by state data that shows that only 15 percent of the 6,540 voters who used out- of-state driver's licenses have since acquired New Hampshire licenses.