The deal is for 14 years and is worth about $100 million, a source confirmed to ESPN.com.
A restricted free agent, Weber has spent his entire career with the Nashville Predators, who have seven days to match Philadelphia's offer, which was first reported by TSN of Canada.
If the Predators decide not to match the offer, they would receive four first-round draft picks from the Flyers, according to TSN.
Predators part owner W. Brett Wilson posted on Twitter, "Am aware of Philly offer."
Weber's departure would be a devastating blow to a team that already lost All-Star defenseman Ryan Suter, who signed a 13-year, $98 million deal July 4 with the Minnesota Wild.
A three-time All-Star and the Predators' captain for the past two years, Weber scored 19 goals and had 49 points this past season while anchoring one of the NHL's top defensive teams.
Weber, 26, has 99 goals and 164 assists in his seven-year NHL career.
Information from The Associated Press was used in this report.
This would be a huge upgrade for the Flyers but 4 first rounders is a heavy price to pay
This post has been edited by seanbrock: 19 July 2012 - 12:13 PM