Sportsnet and TSN reported agent J.P. Barry can speak to other NHL teams to possibly set up a sign-and-trade deal for the defenseman.
The Hurricanes and expansion Seattle Kraken are the only teams that can offer Hamilton a maximum term of eight years. If he signs elsewhere as a free agent after July 28, the maximum contract length would be seven years.
Hamilton said last week that the Hurricanes had yet to resume discussions about re-signing him. He played the final season of a six-year contract he signed with the Calgary Flames on June 30, 2015. He was traded to Carolina on June 23, 2018.
"I let my agent talk, but they kind of tabled conversations until after the season and I'm sure they'll start talking again soon," Hamilton said June 9.
Hamilton led Carolina defensemen and tied for seventh in the NHL with 42 points (10 goals, 32 assists) in 55 games. He scored 18 power-play points.
"I really enjoy it here," Hamilton said. "I've got some really good friends, met really, really good people in the room and away from the room off the ice too. I have nothing bad to say about my experience here and being a Carolina Hurricane and I've really enjoyed it. Hopefully we can keep going."
The Hurricanes (36-12-8) lost the Stanley Cup Second Round in five games to the Tampa Bay Lightning after they were the No. 1 seed in the Discover Central Division. Hamilton scored five points (two goals, three assists) in 11 Stanley Cup Playoff games.