Zibanejad, 23, has spent his entire career so far with the Senators, registering a total of 64 goals and 87 assists for 151 points in 281 career regular season NHL games since being drafted by Ottawa in the first round (sixth overall) in 2011.
The Swedish forward set career-highs in games played (81), goals (21), assists (30) and points (51) last season.
Zibanejad has one year left on his two-year, $5.25-million deal, which carries a $2.625-million cap hit, before he becomes a restricted free agent.
Brassard, meanwhile, has three years left on the five-year, $25-million contract he signed with New York in July 2014.
Brassard, also a sixth-overall draft pick (Columbus, 2006) spent just over three seasons with the Rangers, and led the team in goals (27) in 2015-16. He also ranked second in points, with 58, behind Mats Zuccarello.
The 28-year-old native of Gatineau, Que. has recorded 127 goals and 216 assists for a total of 343 points in 563 career NHL regular season games split between the Blue Jackets and Rangers.