Asked if forward Andrew Copp was making a good case for a bigger role with the club, Maurice mocked Laine's recent comments regarding his lack of top-line minutes.
"Did he tell you he wants to play with our best players?" Maurice said of Copp, according to The Athletic's Murat Ates.
In an interview with Finnish outlet Iltalehti published Monday, Laine suggested he would be a first-line player on most NHL teams.
"When you're having contract negotiations, one thing always is who you are playing with," Laine told Iltalehti's Pekka Jalonen in Finnish. "With the merits I have, somewhere else I'd have an opportunity to play with the best players. Everybody who understands hockey knows that."
Maurice is well aware of Laine's desire to shoulder more responsibility with the Jets, but the 52-year-old bench boss preached patience for his younger talents.
"What Patrik and (Nikolaj) Ehlers and Kyle Connor and all the others are attempting to do, they just want to play more," Maurice said Tuesday, according to NHL.com's Tim Campbell. "And there's going to come a time for all three of them that they'll turn around and say, 'See, I told ya. If you'd just played me more.'"
"And I'll use my driver's license analogy: Nobody gets the keys at 14."
Laine, 21, is coming off a career-low 50-point campaign in 2018-19 and is currently skating with Swiss club SC Bern as his contract dispute with the Jets continues.