The trade that brought Jaromir Jagr to the Boston Bruins from the Dallas Stars near the NHL Trade Deadline wound up costing the Bruins their first-round pick because they made the Stanley Cup Final.

One day before the 2013 NHL Draft in Newark, N.J. (3 p.m. ET; NBCSN, TSN), Boston general manager Peter Chiarelli said he'd like to find a way to get back into the first round.

"I think any GM who went into the draft without a first-round [pick] would have to do that," he said Saturday when asked if he'd like to acquire one. "So -- of course I would. Yes."

Regardless of where the Bruins draft, Chiarelli said the team's philosophy continues to be to pick the best player available, regardless of position.

"That is always is the overriding thought and objective," he said. "When you get into the nitty-gritty of who's at [No.] 10 or 11 and why, you've got to look to need a little bit. But the overriding tiebreaker and the overriding mentality is best player available."

The biggest offseason priority for Chiarelli is re-signing goaltender Tuukka Rask, who will become a restricted free agent July 5. That could be difficult, because the NHL salary cap is expected to drop to $64.3 million for the 2013-14 season; the Bruins sit less than $5 million below that.

Chiarelli expressed in his season-ending press conference Wednesday that the Bruins would like to re-sign Rask "as soon as we can." Rask has said he wants to stay with the Bruins.

Chiarelli said Saturday the team has made a qualifying offer to Rask, as well as to prospects Jordan Caron (forward) and Michael Hutchinson (goaltender). No offer has been made to forward Kaspar Daugavins, who is arbitration-eligible. So is Rask, but that's not an avenue Chiarelli wants to explore.

"I don't want to go to arbitration with [Tuukka]," he said. "I’ve talked to his agent, and we’re trying to work something out."

Two unrestricted free agents who won't be back are forward Nathan Horton and defenseman Andrew Ference. Horton's agent said Saturday he wants to go to another team, and Chiarelli announced this week that Ference wouldn't be re-signed due to salary-cap constraints.

Chiarelli said he would do what he can to help Ference find a new team.

"I’ve got a couple of teams on Andy, and I’ve spoken with Andy’s agent in order to help out, and I’ve actually given Andy’s agent permission to talk to teams and then come back," Chiarelli said. "I’m not going to stand in his way; as I said it at my press conference before, he’s been a warrior for us, and I want to help him as much as I can."