Several reports said a trade was close, possibly with the New York Islanders. Parise's father, J.P. Parise, played for the Islanders from 1974-78 after eight seasons with the Minnesota North Stars (1967-75). J.P. Parise died in 2015.
Parise, who was born in Minneapolis, said he knew the possibility of a trade existed for the past week and the thought of leaving his home state was weighing heavily on him.
"It was a pretty stressful day yesterday," he said. "It wasn't uncomfortable showing up to the rink today. I think players understand these types of things happen. So there was no issue there. But yeah, yesterday was pretty stressful."
Wild general manager Bill Guerin, who took over for Paul Fenton on Aug. 21, 2019, said Monday he explored an opportunity to trade Parise, who has 37 points (21 goals and 16 assists) in 61 games this season, but nothing came of it before the deadline.
"Look, Zach and I have a good relationship," Guerin said Monday. "We've talked over the last week about certain possibilities. We were both completely up front with each other and honest with what was going on or feelings or anything like that. The fact that nothing happened today is fine. This is something that we're just looking forward on now. Zach's a big part of the Minnesota Wild and he's going to be and we're excited to still have him."
The Wild (29-25-7) are five points behind the Arizona Coyotes and Calgary Flames for the first wild card into the Stanley Cup Playoffs from the Western Conference. Minnesota did not make the playoffs last season after qualifying in each of the previous six.
"I'm thinking about the Blue Jackets and winning this game and closing that gap in the playoffs," Parise said.
NHL.com independent correspondent Jessi Pierce contributed to this report