SOG: 8 | +/-: -1
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 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.