Now that the regular season is over, Nuggets general manager Tim Connelly is focusing full-time on a search for a new head coach.

“I think it’s a chance to get to know a lot of different candidates,” Connelly said Thursday. “And then when we find the right fit, we’ll be aggressive and pull the trigger.”

Names expected to get attention include former NBA coach Mike D’Antoni, current Golden State assistant Alvin Gentry and college coach Billy Donovan, in addition to Melvin Hunt, who has been the Nuggets’ interim head coach. A wild-card could be Oklahoma City coach Scott Brooks, if the Thunder decide to part ways with him.

“We’re going to be pretty patient,” Connelly said. “Certainly Melvin is going to be one of the finalists. I think he deserves that, he’s earned that. But we’re going to talk to anybody and everybody, candidates that could potentially help us take the next step. So we’re in no rush.”

The new coach will be asked to keep the pace of play high, and that may eliminate candidates known for favoring more of a half-court style or skewing heavy on defense. That’s in contrast to the Nuggets’ philosophy when they hired Brian Shaw, who was fired March 3 and replaced by Hunt.

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“I’m not a coach,” Connelly said. “But I do think we’re Denver. We’ve got to play with pace, we’ve got to play up-tempo basketball. And up-tempo basketball can take on various styles. We’re certainly looking for a coach that understands how we’ve been successful in the past and probably how we’ll be successful in the future, with fast basketball and playing with pace.”

Hunt led the team to a 10-13 record. Under his leadership the Nuggets played much better at the offensive end than they did under Shaw.

“Melvin did great,” Connelly said. “Melvin was fantastic and so was his whole entire staff. Certainly one of his greatest attributes is his love for the game and the positivity that he exhibits every day. I think you saw that on the sideline. I’m unbelievably proud of him and he certainly wasn’t handed an easy situation.”

WATCH: What’s next in Denver Nuggets’ search for a head coach?

Connelly does not have a specific timetable for the hire except that he wants a coach hired before the NBA draft on June 25.

“We have internal lists, and those guys are guys that we’ll start to be a little more proactive in reaching out to,” he said. “On that list is a guy that’s going to be deep in the playoffs, and it’s a guy that’s worth a conversation. We don’t want to put any unnecessary internal timeframes on it.”

Christopher Dempsey: cdempsey@denverpost.com or twitter.com/dempseypost