Could new Rangers coach put BU star on their draft radar?

David Quinn came into the job as the 35th coach in Rangers history with a couple of important preexisting relationships — but a future reuniting might be the most interesting.

When Quinn left Boston University after five years as head coach, he also left 18-year-old winger Brady Tkachuk, whom many believe will be a top-five pick in June’s entry draft. The son of longtime NHLer Keith Tkachuk, Brady just finished his freshman year at BU, and Quinn sees all the skills for him to be a successful pro.

“I think he’s going to be a great player at the NHL level,” Quinn said at his introductory press conference on Thursday at the Garden. “He has all the tools. I think people get enamored with his physical play, but he’s a talented player. Great skill, great vision, he skates well. There’s an awful lot there.”

After the Lightning lost to the Capitals in Game 7 of the Eastern Conference final on Wednesday, the draft order for all three of the Rangers’ first-round picks was set. They own No. 9 (their own), No. 26 (from Boston) and No. 28 (from Tampa Bay). They also have two second-round picks and two third-round picks, a nice little bushel if they choose to try to move up.

Despite his attachment to Tkachuk, Quinn wasn’t going to spend his first day on the job making any assumptions about his input regarding the draft process.

“Gordie Clark does a phenomenal job,” Quinn said about the team’s director of player personnel. “If they want to ask me any opinions, I’m there as a resource.”

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Quinn said he made the decision to take this job on Thursday or Friday, so he hasn’t quite gotten around to thinking about who will round out his coaching staff. He did grow up in Cranston, R.I., with former Islanders coach Jack Capuano, currently an assistant with the Panthers — but those decisions are still probably a ways off.

“I want to make sure we do it the right way and go through the process to make sure we get the right people to round out the staff,” Quinn said. “The sooner the better, but I don’t want to sacrifice anything just to have a staff.”

As the Rangers have declared their team in a rebuilding mode, Quinn was asked about veteran goaltender Henrik Lundqvist, now 36 years old with three more years left on his contract at an annual salary-cap hit of $8.5 million.

“Henrik is one of the best goalies in the world,” Quinn said. “No one is more competitive, no one works harder. I’m excited to have him as our goalie.”

Quinn said he gets mistaken for looking like current Penguins coach (and former Rangers assistant) Mike Sullivan “15 times a day.”