The subject was Brian Leetch, and Brady Skjei’s eyes were as big as saucers.

Skjei has always admired Leetch’s legacy, even though Skjei was less than three months old when Leetch lifted the Conn Smythe Trophy and the Stanley Cup.

The point was this – even the greatest offensive defensemen of all-time had to learn to take risks, to not be afraid to make a mistake, but also to figure out how to turn those risks into high-percentage plays.

Skjei, who turned 23 on Sunday – when he scored a goal on his birthday – is going through that lesson as a rookie, arguably the most important and influential rookie in the Rangers’ lineup this season.

Leetch – whom Skjei has yet to meet – went through a process too, though he was farther along, a Calder Trophy winner his first season and a sure-fire star in the making. As he played, he figured it out and when Mark Messier got in his ear about being unafraid to take a chance, his star streaked to the Hall of Fame.

“That’s obviously one guy I’ve looked up to,” Skjei said. “He’s just an unbelievable defenseman and it’s fun to watch highlights of the way he played the game, just the way he moved the puck, skated the puck up the ice. You’ve got to play with that swagger and confidence.”

Skjei, who had a cup of coffee with the Rangers during last season, then out of necessity wound up on the first defense pair in the playoffs, trained over the summer with Rangers captain Ryan McDonagh and alternate captain Derek Stepan in Minnesota.

They told him, “Just play your game. Do what got you here because you’re here for a reason.”

“That’s the main thing,” Skjei related. “They said there was going to be ups and downs, so don’t get too high, don’t get too low. Stay kind of even-keeled and you should be fine.

“A lot of it is just confidence. When you’re playing free and not worried to make a mistake, that’s when you’re at your best. When you start thinking a little too much, that’s when things start creeping into your game. So confidence is a huge thing, but the top defensemen who have offense in their game kind of play with that swagger, that confidence, that they’re not afraid to make a mistake.”

McDonagh is the type of player who matches Skjei’s skill set – a big, strong player whose skating and ability to lug or pass the puck out of trouble are his best attributes.

And before we go any further here, let’s be clear, nobody is comparing Skjei to McDonagh, much less Leetch, at this early stage. But the first-rounder (28th overall in 2012) has potential to be something special.

“When you look at Brady Skjei, first of all, I think you have to be patient with any young guy that comes in,” said MSG Networks analyst Dave Maloney, who knows about being a young defenseman in the NHL – he was the youngest captain in Rangers history.

“Lots of times a guy come in and there are all kinds of expectations, given what he did in the playoffs a year ago. I chuckle after speaking with him. You know, he only had 14 points his best year as a collegiate player (at the U. of Minnesota). He comes up late last year and they bring him into Pittsburgh (for the first-round playoff) and now he’s on the power play. He told me that he got calls and texts from his buddies, like, ‘How does that work? You get 14 points your best year and now you’re on the power play in the Stanley Cup playoffs.’

“I think there’s an offensive side to Brady, there really is. But his whole game is predicated on his skating. Once he learns to use the basis of his skill sets, then he’ll become an even more dynamic player. In this day and age, anybody who can move like he does and then take it to the next step by moving the puck, he’s going to be that much better. And also too, from the get-go, we’re seeing a guy that was actually encouraged to use his skills.”

Maloney credits Leetch’s former partner, Jeff Beukeboom, who coached Skjei in Hartford of the AHL last season, and who is the Rangers’ assistant coach in charge of defensemen this season.

“You are who you are,” Maloney said, “and I think that’s Jeff Beukeboom. You go back to Day 1, where he never got off the ice when he was in Hartford. He was on the power play, penalty kill, and all those things. So I think we’re seeing a natural progression of that from him. I think the next step for him is, can he recognize offensively what he’s been able to create? That intangible that guys like Leetch, guys like (Erik) Karlsson, guys like (Drew) Doughty – the elite defenders now have to have some sort of offensive game. It’ll be interesting whether Brady matures – and I don’t know if that’s nature or nurture or whatever it is – but he certainly is bright enough and has all kinds of skills for this day and age the way the game is being played.”

Skjei said he was asked to play a different, non-offensive role in college, and that he got the chance to play on both ends of the ice, to use his offensive skill, in Hartford. That, he said, “translated well” into this season.

Skjei became the fourth Rangers defenseman in history to rack up 30 or more assists in his rookie season, joining Leetch, Reijo Ruotsalainen and Ron Greschner. That is something that has only been done twice in the entire NHL since Skjei’s birth year (John Carlson and Tyler Myers are the others). Skjei ranks fourth among all NHL defensemen, and tied for first among all NHL rookies, with 25 even-strength assists.

“This is a real good opportunity for him,” Rangers coach Alain Vigneault, whose system requires skaters and puck-movers, said. “He has to stay focused and continue to work on his game both offensively and defensively. We have said many times that there is a tremendous amount of skill there and he has to continue. The more he works on his game, the more he understands it and the better the decisions he will make with the puck. And that is what we need from Brady.

“As a defenseman, you need to make the play that is in front of you and you need to play the percentages a bit. You need to know when it’s time to jump in the rush and when it’s not time — not trying to make something out of nothing in front of you. That (comes) with experience and Brady, this year, has gotten a fair amount of ice time. He has earned that ice time and he will continue to get better.”

Skjei, while working out with McDonagh and Stepan, convinced himself that he did not have a job at all guaranteed when he came to training camp, and he had a woeful camp and preseason, mainly because he was sick for most of it.

He battled through that and started to take off in the right direction when the season began.

It helped, too, that he roomed up with rookie forward Jimmy Vesey, the two share an apartment in Manhattan and are also roommates on the road. They have fun, enjoy being young men in the big city and on the big stage, and they also bounce rookie stuff off each other.

“Tons of stuff,” Skjei said. “It’s nice that we’re doing it together. The car rides and sitting around the apartment. If you’ve got to ask a question, it’s pretty easy. Just trying to figure it out. The older guys are helping us out a ton. They’re doing a pretty good job.

“Yeah, it is (a roller coaster). You’ve got to come to play every day. Otherwise, there are guys who will take your spot. It’s up and down, but it’s nice to have someone to hang out with, and talk to, and keep a level head.”

Skjei’s head, like Vesey’s, is level. He, like Vesey, wants to be difficult to play against in addition to using his skill (he’s second on the team in hits and a strong kid who could still get stronger).

“He’s had an impressive year,” Marc Staal said. “He’s gotten better, more comfortable, as the year’s gone along. He’s a talented guy. It’s been fun to watch him.

“As a young guy, early on, I told him he can’t over analyze a bad shift, a bad game. When you play as many games as you do, you’ve got to try to stay as confident as possible and move on and play the next day, and start over and come to the rink with a positive attitude. If you start beating yourself up too much, it can go downhill on you. I think he’s done that. He comes to the rink, comes to work. He’s a positive guy and I think that’s helped him throughout the year, and it’s helped our team.”

“Definitely, you can tell he’s got his head up a lot more with the puck,” McDonagh added. “He understands what his strengths are, his skating ability, his ability to get away from forecheckers and oncoming defenders. He gives himself more time when he uses his legs as opposed to getting a puck and freezing out there, trying to find somebody standing still. He’s moving his legs, he’s creating space and then he’s able to find the next play for himself.

“It’s a great sign for us.”