Christie, who is well back in the pack seeking the Republican nomination for president, told a campaign event in the early voting state of New Hampshire that he would ask FedEx Chief Executive Officer Fred Smith to devise the tracking system.
Immigration has become a top issue in the Republican campaign, with front-runner Donald Trump vowing to deport all of the estimated 11 million illegal immigrants and to build a wall along the southern border.
"At any moment, FedEx can tell you where that package is. It's on the truck. It's at the station. It's on the airplane," Christie told the crowd in Laconia, New Hampshire. "Yet we let people come to this country with visas, and the minute they come in, we lose track of them," he said.
"We need to have a system that tracks you from the moment you come in, and then when your time is up ... however long your visa is, then we go get you. We tap you on the shoulder and say, 'Excuse me. Thanks for coming. Time to go,'" Christie said.
He said 40 percent of illegal immigrants are allowed into the United States legally with a visa and then overstay their visit.
Christie has been lagging in recent opinion polls and is in danger of not making the top 10 candidates who will participate in the next official Republican debate on Sept. 16.
With real estate mogul Trump taking a hard line on illegal immigration, other Republican candidates in the 2016 White House race have sought to toughen their stances as well.
Christie did not say specifically how the system he proposes would track people the same way packages are tracked by FedEx, which scans a bar code on the package at each step in the delivery process.
A FedEx spokeswoman