Streit, who can become an unrestricted free agent in July, reportedly turned down what the team had termed its best offer, and will allow Streit to hit the open market.
The 35-year-old blueliner had 27 points in 48 games last season, his fourth with the team, and had five points in the team's six-game, first-round playoff series loss to the Pittsburgh Penguins.
He had been team captain since the start of the 2011-12 season.
Streit has 288 points in 491 NHL games with the Montreal Canadiens and the Islanders.
The newspaper also reports John Tavares is likely to take over as captain for Streit; goaltender Evgeni Nabokov is likely to re-sign before July 5; and forward Brad Boyes is unlikely to return as he seeks a long-term contract, though talks with the Islanders are ongoing.
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