Parise has missed two games since reaggravating an injury he sustained Nov. 25.
"He wants to be in the lineup. Hopefully every day he gets his rest is a day we get closer to him coming back," coach Mike Yeo told the newspaper. "He wants to get on the ice and he wants to help the team. He's a huge part of our team. We can't wait to have him back."
Parise was expected to miss up to three weeks after he sustained the injury blocking a shot against the St. Louis Blues. He sat out one game before returning, and perhaps playing that soon caused the injury to worsen. The Pioneer Press said he was evaluated over the three-day Christmas break.
Parise has 15 goals and 12 assists in 37 games, but four goals and one assist in 12 games since the injury. The Wild are 5-9-1 over that time (12 games played, three missed).
Parise is expected to be named to the United States Olympic team when that roster is announced Jan. 1, 2014. There is no indication if he will miss that event in February.