The tag guarantees Norman $13,952,000 in 2016 if he and the team can't agree to a long-term deal by July 15.
"I'm excited that Josh will be back with the Panthers next season," head coach Ron Rivera said in a statement from the Panthers. "He played very well for us this year and was a big part of the success we enjoyed as a team."
The Panthers and Norman's agent, Mike George, began discussing a long-term deal on Thursday night at the NFL scouting combine in Indianapolis, according to a league source. The sides, according to the source, weren't initially close, as Norman is seeking a four- or five-year deal worth an average of around $14 million a year.
The top corners in the NFL -- the New York Jets' Darrelle Revis, the Arizona Cardinals' Patrick Peterson and the Seattle Seahawks' Richard Sherman -- each are making just over $14 million a season. Norman, 28, turned down a multiyear deal that averaged more than $7 million a year prior to the 2015 season, according to sources.
His stock skyrocketed in the first four games as he intercepted four passes, returning two for touchdowns. Teams ultimately began to avoid throwing in Norman's direction.
Opposing quarterbacks had a rating of 54.0 when throwing in Norman's direction during the regular season. No other cornerback had a better rating, according to Pro Football Focus.
When a player is tagged with the non-exclusive franchise tag, the team has the right to match any offer he receives. If the player signs elsewhere, the signing organization would have to send two first-round draft picks to the original team.
Norman recently told ESPN he wouldn't take it personally if the Panthers used the franchise tag that prohibits him from becoming an unrestricted free agent.
"It's a business, at the end of the day, and nothing is ever personal,'' Norman said. "It's not personal with them. It's not personal with Coach [Rivera] or position coaches. Nothing is ever personal.''
Rivera said last week at the combine that he was optimistic that a deal could be reached with Norman. He expects Bene Benwikere will battle for the starting job opposite Norman.
Benwikere has been primarily a nickelback, but he played well as the every-down corner for four games when veteran Charles Tillman was out with a knee injury. Benwikere's season ended prematurely when he fractured his left leg in the second half of a Dec. 13 win against Atlanta.
Norman has played football his entire life in North and South Carolina. He grew up in Greenwood, South Carolina, and played college ball at Coastal Carolina in Conway, South Carolina.
The Panthers selected Norman in the fifth round of the 2012 draft.
Norman said he would like his career to continue at Carolina, but said ultimately a long-term deal will depend on the numbers, since his age means this is his only real chance at a big contract.
"If you're the best at something, obviously, you want the things to show for it,'' Norman said. "But at the same time, I love where I'm at and I don't want to change it.''