LOS ANGELES -- There was the 40-year-old Martin Brodeur chatting briefly the 26-year-old Jonathan Quick in the handshake line after the Kings captured the Stanley Cup with a 6-1 victory in Game 6 at Staples Center on Monday night.

Only it wasn't the wise, veteran Brodeur doing all the talking; it was Quick doing most of the whispering into the future Hall-of-Famer's ear.

What was the Conn Smythe Trophy-winning Quick telling Brodeur?

"He wanted to make sure I don't retire," Brodeur said. "I guess he likes beating me."

Brodeur, who will be an unrestricted free agent July 1, said he has yet to decide if he wants to come back next season, but he gave every indication that he wants to return to New Jersey if he returns.

"I want to play … I think I want to play," Brodeur said. "I'll talk to my little girl and see what she thinks. I'm sure she's going to want to see me play. The Devils is what I am, it's what I believe in and this is where I want to be."

However, Brodeur didn't close the door on possibly playing for another team; but said it would take something crazy for that to happen.

"I don't see myself at all doing that, but I think circumstances are out of my hands," Brodeur said. "You never know, I guess. But you don't want to. It'll definitely have to be something really, really weird that I'm going to do that."

It was a renaissance season for the Brodeur, who enjoyed his most successful Stanley Cup Playoff run since winning his third Stanley Cup in 2003. He had a 2.12 goals-against average -- his best since 2003 -- and a .917 save percentage while winning 14 games. In the regular season, Brodeur won 31 games with a 2.41 GAA and .908 save percentage and looked like his vintage self during the second half.

Brodeur has four Vezina Trophies, two Olympic gold medals and just about every record a goaltender could own, but he said he needed to prove to himself that he could still play at a high level in the NHL.

"I think this season and this playoff run answered a lot of questions about where my game is at and I'm really happy to hopefully continue," Brodeur said. "I want to be the best I can be and I think my expectations are higher. I want to be able to contribute and play at a certain level and play a lot of games and not take a seat and not play. I've learned this year to take it easy at times and work hard, a lot of different things I didn't have to do when I was younger. I think it paid off in the end in the way I was able to finish the season and throughout the two (playoff) months I played.

"I feel real good. I was two games away from winning a Stanley Cup. There were a lot of clutch games I needed to play well and I did. I like the team in front of me and the system that we play in. That really helps my game as far as handling the puck and doing different things. This season kind of put a little more jump into what I wanted to do and try to continue a little more. But we'll see. I'm not sure yet."

Brodeur isn't the only top priority for Devils GM Lou Lamoriello, as captain Zach Parise will also be an unrestricted free agent July 1. Brodeur said what Parise decides won't affect him, but he believes the franchise needs to lock up the star forward before turning its attention to him.

"I think Zach is a big thing that the organization has to take care of first," Brodeur said. "There's no doubt about that. I think they need to try to lock him in, lure him into staying. He's a franchise player. He's a guy the fans love and as a captain, he's a great leader and did a great job in his first year as captain to bring a team that was counted out early in the season almost to what we accomplished, it's pretty impressive."

The reinvigorated Brodeur said one reason why playing another season is so enticing is the developing young core of the Devils, which includes Adam Larsson, Adam Henrique, Jacob Josefson, David Clarkson and Parise.

"It's huge," Brodeur said. "Seeing young players like Henrique, Clarkson and Zach and a lot of different guys out there and Larsson is going to come to be an unbelievable defenseman. Jake is going to do well. It's not just young players, but middle-tier players. I think we found ourselves depth through trades and stuff. I know every year it's hard to keep teams together. Hopefully we'll be able to make the necessary moves to keep these guys and hopefully I'll be a part of it."

A reason Brodeur is leaning toward another season is his rediscovery of what it's like to be part of a deep playoff run. Before missing the playoffs last season, the Devils were knocked out of the playoffs in the first round in three straight seasons. Getting a taste of playoff success may have given Brodeur more motivation to keep playing for as long as he can.

"The last few years, it's been tough in the playoffs for us, so you lose the feeling of what it is to win even though you win in the regular season," Brodeur said. "Playoff series is when you have that thing inside of you, and I think I got it back. It was pretty cool this season."

Follow Dave Lozo on Twitter: @DaveLozo