Staal led Minnesota with 42 goals last season, the most he has scored since he had 45 with the Carolina Hurricanes in 2005-06.
"I've let it be known that I've enjoyed it and I'd like to stay," Staal said during the NHL Player Media Tour on Thursday. "I think it's a great fit for me hockey-wise. They're a team that wants to win the Stanley Cup real bad and so do I. Hopefully it's a situation where I can stay and try to be a contributor to do that, but again, that's something we'll see how it plays out in the next little bit."
Staal said his situation with the Wild is different from three years ago, when he was in the last season of a seven-year contract with the Hurricanes and was expecting to be traded because Carolina wasn't supposed to be a Stanley Cup Playoff contender. He was ultimately traded to the New York Rangers on Feb. 28, 2016.
Staal doesn't think he'll have to worry about the same thing with Minnesota this season, even if he is still without a contract around the 2019 NHL Trade Deadline.
"This is a team that expects to win," Staal said. "That makes it a different situation just for me, my own mental side. In Carolina, I could see the writing on the wall and it was one of those things where we were kind of methodically going through the months to get to the point where it was time for me to move on. It doesn't have that same feel."