He wants his players to grow.
In the case of many of his players, McLellan is looking for growth in their skill levels, their willingness to venture into tough areas on the ice, their desire to apply themselves at both ends of the rink.
"I really believe," McLellan said, "that once you stop growing, you start decaying."
But there is one player who literally is trying to grow.
Here's a hint: His nickname is Little Joe.
At 5-foot-11, 190 pounds, 26-year-old center Joe Pavelski is not tiny by everyday standards.
But given the job description of a smallish NHL player -- battling for loose pucks and working along the boards against opposing players a half-foot taller and 30 pounds heavier than he is -- Pavelski can use all the size and strength he can muster. His goal is to improve his ability to maintain control of the puck even if those trying to take it from him are bigger and taller.
"Puck protection comes with strength and working on strength is always big," said Pavelski, who is preparing to begin his fourth NHL season. "There are a lot of big, strong guys in the league."
It was at his first NHL camp that Pavelski fully realized what he was up against when he battled for a puck with then-Sharks defenseman Kyle McLaren, who is 6-4, 235 pounds.
"I remember how big he was," Pavelski said. "There was definitely a learning curve."
Though Pavelski recognizes his key shortcoming, there's plenty to love about the player he already is.
He posted career highs with 25 goals and 59 points last season, and was fourth in the league in faceoff percentage, winning 58 percent of his draws.
But he was just getting started. Pavelski led the Sharks in scoring during the playoffs, recording 9 goals and 17 points. He averaged 21 minutes, 32 seconds in the postseason, more than Joe Thornton and more than any forward on the team besides Patrick Marleau.
And that doesn't even take into account Pavelski's strong performance during the Winter Olympics, as the United States came within a Sidney Crosby overtime goal of winning a gold medal.
"He's a very detailed player," San Jose General Manager Doug Wilson said of Pavelski, a Wisconsin native. "You saw what he's capable of doing offensively last year. He plays in all zones. He plays the point on the power play. He's a very mature player."
McLellan said he fully believes Pavelski is capable of taking his game to an even higher level this season and increasing his strength and power.
"I think it's very realistic," McLellan said. "And it's interesting. When you ask players, they're the first to know where they need to grow. When they know themselves where they have to improve, it's powerful. When we have to drag them in and sit them down and tell them and beg them to improve in an area, it's not so powerful."
No one has to drag Pavelski in for such talks. It's a key focus for him.
As a result, he's viewed by many around the team as one of the leading candidates on the Sharks to replace retired defenseman Rob Blake as captain. A decision is forthcoming, to be made by a collaboration of the coaches and players.
"He plays a really well-rounded game," Wilson said. "He helps in all areas of the rink and he's always inquisitive. He likes talking about ways to improve."
Pavelski would relish the chance to wear the "C."
"It would mean a lot to any player," he said. "It would be a huge honor if it was to come."
Given a choice, however, between the "C" and the Cup, the answer is obvious.
"We took a step in the right direction," Pavelski said, thinking back to last season. "There was a hump we got over. But it's obviously not the hump you want to get over. We have to take what we learned from that and try to apply what we learned. Obviously there's a way to top last season. We want the end result."