"It's quite an honor, I'd have to say," Sullivan told SN590's "Hockey Central" on Wednesday. "He's a privilege to coach. … It makes my job easy when our best player and the best player of his generation is the hardest-working guy and the most driven guy on the ice, and off the ice, for that matter."
Sullivan added, "He for me epitomizes an athlete that controls everything within his power to be his very best. And when you have a guy like that on your team and he's your captain and the best player in the game, it certainly makes the coach's job a whole lot easier."
Sullivan joined the Penguins as head coach in December 2015 and went on to win the Stanley Cup the same season. He then led the Penguins to a second consecutive Cup victory.
Crosby took home the Conn Smythe Trophy both years, recording a total of 14 goals and 46 points across both playoff runs.
When asked whether he believes Crosby will become a coach, Sullivan said yes.
"If he wanted to be a coach, I think he would be a terrific coach because he is such a student of the game," Sullivan said. "That's something that I think would be a personal decision from his standpoint, but if he does choose to go down that path, I think he would be terrific at it.
"It wouldn't surprise me one bit when Sid's done playing the game somewhere down the line, but I don't see that happening anytime soon because he loves the game as much as he does."
Crosby, who turns 33 this summer, has had one of the league's most illustrious careers to date. He owns two Hart, Art Ross, and Rocket Richard Trophies, and has been awarded the Stanley Cup three times. He's racked up 462 goals and 1,263 points in 984 career regular-season games.