"We talked when he took the job over. We said, 'You know what? Let's get us through the regular season. Let's get through the playoffs, and we're going to sit down and talk,'" Nill told Sportsnet. "But he's earned it, and I hope that down the road he wants to be the head coach."
The Stars, who promoted Bowness Dec. 10, are one win from reaching the Stanley Cup Final after defeating the Vegas Golden Knights 2-1 in Game 4 of the Western Conference Final on Saturday.
Game 5 of the best-of-7 series is at Rogers Place in Edmonton, the hub city for the conference finals and Stanley Cup Final, on Monday (8 p.m. ET; NBCSN, CBC, SN, TVAS).
Nill three days ago said the sides would wait until the season was complete before addressing Bowness' status.
At 65, he's the oldest coach in the NHL.
"I just be me with the players," Bowness said this week. "That's how I've always coached. I'm not one of those guys that labels [coaches] player coach, [or] not a player coach. I don't believe in all that stuff. I'm just me. I just do it my way."
Bowness was promoted when Jim Montgomery was fired for unprofessional conduct. Montgomery said Jan. 3 he had been receiving counseling for alcohol abuse and had checked himself into an in-patient residential program.
The Stars were 20-13-5 after the coaching change. They advanced to the conference final by defeating the Calgary Flames in six games in the first round and the Colorado Avalanche in seven games in the second round.
Dallas last made the Stanley Cup Final in 2000, when it lost to the New Jersey Devils after winning the championship in 1999 by defeating the Buffalo Sabres.
"When we had to make the change, everything went pretty quick," Nill said Wednesday. "We went right from having to make the coaching change to Rick taking over, and then all of a sudden you get a pandemic. That gave him a chance to reset, and I think we're reaping the rewards right now of him having a chance to put his stamp on this team. I've been very impressed."
Nill said Bowness' positive impact is obvious by how the Stars respond to him.
"When you see the players react to a coach and decisions he has to make, that's important," Nill said. "I know Rick has the full support of the players, and that's very important."
Dallas center Tyler Seguin said it's clear to the players that Bowness is in charge and they appreciate how he works with them.
"He's one of those guys that you want to win for," Seguin said.
Bowness had not coached a team since he replaced Bob Francis for the final 20 games with the Phoenix Coyotes in 2003-04. Since then, he's been an assistant with the Coyotes, Vancouver Canucks, Tampa Bay Lightning and Stars.
He's 142-302-8 with 48 ties as a coach with the Stars, Coyotes, New York Islanders, Ottawa Senators, Boston Bruins and Winnipeg Jets, and 20-15-0 in 35 postseason games.