The forward, who can become an unrestricted free agent, is allowed to talk to other teams beginning Sunday and could still sign with Dallas, which acquired him in a trade from the New York Rangers on Feb. 23 for two conditional draft picks.
"We've talked a little bit with his agent, but he wants to test the free-agent market and he's got that right," Nill said at the 2019 NHL Draft. "So they're going to look into the market and see what else is out there and then we will swing back and see where he's at.
"We've got an interview period that starts Sunday, so we'll start talking to other people and he'll do the same thing and we'll see where things go."
Zuccarello had three points (one goal, two assists) in two games with the Stars after he had 37 points (11 goals, 26 assists) in 46 games with the Rangers; he sustained a broken arm in his first game with Dallas on Feb. 4 and missed five weeks, and had 11 points (four goals, seven assists) in 13 Stanley Cup Playoff games.
Signed by New York as a free agent on May 26, 2010, the 31-year-old has 355 points (114 goals, 241 assists) in 511 NHL games in nine seasons with the Rangers and Stars, and 42 points (15 goals, 27 assists) in 73 playoff games.
