Modano, 40, is eligible to be a free agent as of Thursday but last week said he hadn't decided whether to retire to try to join another team if Dallas didn't re-sign him.
Dallas General Manager Joe Nieuwendyk Tuesday said the Stars wouldn't seek to sign Modano.
"We have the utmost respect for Mike Modano," Nieuwendyk said. "He will always be a huge part of this hockey club. He is a great teammate and a great person. Mike is the face of this franchise. That's what makes this decision so hard."
Modano was the first overall pick in the 1988 NHL Entry Draft and spent his entire career with the franchise, which was the Minnesota North Stars when he was drafted. He owns team records for goals (557) and assists (802). His point total of 1,359 is the record for an American-born player.
He helped the Stars to the team's only Stanley Cup title in 1999.
Celebrity Families of 2014 [PHOTOS]