Streit played four seasons with the Islanders, missing an entire campaign in 2010-11 due to a shoulder injury.
The Swiss defenceman was remarkably consistent for the Isles when he played, averaging 10 goals and 36 assists per season, and he served as captain the past two seasons.
The Flyers hold Streit's rights until July 5, when he is scheduled to become an unrestricted free agent, and can negotiate a new deal with him exclusively until that date.
"I'm pretty confident," Streit said when asked about the chances that he'll reach a deal with the Flyers. "Maybe they need a few days or weeks, but I'm pretty positive. It'd be awesome to play for the Flyers. The future is bright. They were in the (Stanley) Cup finals three years ago and there is so much skill and a great mix between veteran players and young players, so I'm pretty confident.
"I truly hope it's going to get done soon."
Streit, 35, signed with the Islanders in 2008 after playing three seasons for the Montreal Canadiens. He led the Isles in scoring that year with 56 points and was selected to appear in his first NHL All-Star Game in 2009.
If he lands a spot with Philadelphia, he would bolster the Flyers' blue-line, which was broken down by injuries last season, which contributed to the club missing the post-season for the first time in six years.
"This year was a short season and they had lots of injuries," Streit said. "That makes it tough. It was a special year because of the lockout. That gave an advantage to some teams and some teams struggled. But when you see the Flyers lineup, it is a playoff team. It's no question to me. I believe the Flyers will be in the playoffs next year. They have the skill and the physical part of it.
"It's a great group and I'd love to join that team."
For his career, he's scored 65 regular season goals and 223 assists in 491 games, with 248 penalty minutes. He made $4.1 million US this season in New York, and scored six goals and 27 points.
"Mark is a player we would have had interest in on July 5th," said Flyers general manager Paul Holmgren. "We now have exclusive negotiating rights and we are hopeful that we can get an agreement in place prior to him becoming an unrestricted free agent."
The Flyers have been the most active NHL team in recent years when it comes to trading for negotiating rights. Philadelphia has made such moves with respect to players like Kimmo Timmonen, Scott Hartnell and Ilya Bryzgalov.
The Islanders also received minor league defenceman Shane Harper in the deal. The five-foot-10 Harper has spent two seasons in the American Hockey League and played junior hockey with Everett in the Western Hockey League.