Burke can’t bask in glow too long

Finally, after it had been flown around in a helicopter above thousands of adoring fans, after it had shown up in television studios and classrooms and at swimming meets, and even had an unannounced late-night stop at a restaurant, the Stanley Cup went to Brian Burke himself Saturday night.

Sort of. The Ducks’ general manager decided to have the coaching staff over to his Yorba Linda home to hold the Cup and relive everything that made all these moments over the last 72 hours possible.

“It was great,” Burke said Sunday. “I remember standing with Gary Bettman and I watched the scoreboard tick down. I said, ‘Man, we’re the champs.’ ”

The Ducks will have the summer to savor their first championship, but Burke won’t be caught up in telling stories and rehashing memories. There’s work to do to keep this team at the top.

No other issue will be as important as the fate of Jean-Sebastien Giguere. The 30-year-old goaltender is in his prime and can be an unrestricted free agent on July 1, when he figures to be the most coveted goalie on the open market. If he’s available.

“The first priority is Jiggy,” Burke said. “I think we want him back. We have to see if there’s something that makes sense.”

Many among the estimated 15,000 at the Honda Center on Saturday for a public celebration voiced their opinion when they chanted “Please sign Jiggy” when the general manager took the microphone.

“That was interesting,” Giguere said with a smile. “For me, I’d love to stay here. Everybody knows that. This is my first pick.

“I’m very confident something good is going to happen and I’ll be able to stay here. Hopefully we can come to an agreement.”

Giguere’s agent, Bob Sauve, was in Anaheim on Wednesday night for the Ducks’ Cup-clinching, 6-2 triumph in Game 5 over the Ottawa Senators. Sauve didn’t respond to a message left at his office in Laval, Canada.

Giguere could command a salary comparable to that of top-tier goalies Roberto Luongo or Marty Turco.

Luongo, who could win the Vezina Trophy next week as the NHL’s top goalie, made $6 million in the first year of a four-year, $27-million deal with Vancouver. Turco is in the midst of a four-year contract with Dallas that pays him an average of $5.7 million.

Neither goalie, however, has matched Giguere’s 31-13 postseason record, which includes a 12-1 mark in overtime. Luongo and Turco also don’t have a Cup or a Conn Smythe Trophy as the most valuable player of the playoffs on their resumes.

After the party Saturday night, Giguere noted that he doesn’t feel obligated to test the market.

“I don’t want to be the highest-paid goalie in this league,” said Giguere, who made $3.99 million this season. “I don’t think I deserve that. There’s a lot of goalies that are better than me. But I think there’s a market there and you’ve got to respect the market too. I have to do it for the other goalies, and I have to do it for myself.”

Factoring into that is Teemu Selanne’s contemplating retirement after adding the only thing missing from his career. Selanne said he will take the next two weeks to think about his future.

Selanne, who’ll be 37 on July 3, has scored 40 and 48 goals the last two seasons and said he wants to make sure that he is dedicated to playing at that level.

Once those situations are ironed out, Burke can turn to addressing his defensive corps. The Ducks have Scott Niedermayer, Chris Pronger and Francois Beauchemin locked up for the next two years, but Sean O’Donnell, Joe DiPenta and Kent Huskins have expiring contracts.

Burke must also decide on whether to keep grinding wingers Brad May and Shawn Thornton. He’ll also have to sign 29-goal scorer Dustin Penner, but the 24-year-old is a restricted free agent without arbitration rights.

eric.stephens@latimes.com