The 23-year-old Bogosian has totaled 34 goals and 69 assists in 297 games, all with the Jets franchise - dating back to the team's days as the Atlanta Thrashers.
Bogosian was invited to U.S. Olympic orientation camp that will take place next month.
Bogosian was the Jets' final restricted free agent. Last week, Winnipeg signed right-winger Blake Wheeler to a six-year, $33.6-million deal. The team also gave restricted-free-agent center Bryan Little a five-year, $23.5-million contract.