The initial meeting between Carolina management and Norman's representation took place on Thursday night in Indianapolis, where both sides were attending the NFL scouting combine.
The source said the sides weren't initially close in terms, increasing the odds that Carolina will use the franchise tag on Norman by the Tuesday deadline.
The estimated tag price for cornerbacks in 2016 is approximately $13.8 million, but that could go up when the NFL sets the final cap number.
General manager Dave Gettleman has said several times since Carolina's loss to Denver in Super Bowl 50 that the franchise tag was an option with Norman.
The 28-year-old Norman, who turned down a multi-year deal of more than $7 million per year prior to last season, made the Pro Bowl in 2015 and was one of the top cornerbacks in the league.
Norman told ESPN on Friday that he wouldn't take it personally if the Panthers used the franchise tag on him.
"It's a business at the end of the day, and nothing is ever personal,'' said Norman, selected out of Coastal Carolina in the fifth round of the 2012 draft. "It's not personal with them. It's not personal with coach [Ron Rivera] or position coaches. Nothing is ever personal.''
Norman said he hopes to stay with the Panthers and is optimistic a deal can be reached. Even if the tag is used, the Panthers have until July 15 to reach a long-term deal.
"I really hope that I can be here, because I've been here my whole life,'' said Norman, a native of nearby Greenwood, Carolina. "I don't want to change that. But hey, you never know how things will go.''