Skinner struggled last season, scoring 23 points (14 goals, nine assists) in 59 games after the forward scored 63 points, including an NHL-career high 40 goals, in 82 games in 2018-19.
The Sabres are hoping Staal, a center and Skinner's former teammate with the Carolina Hurricanes who was acquired in a trade from the Minnesota Wild on Sept. 16, can help him regain his scoring touch.
"I think that's what separates the best players in the League is being able to bring it every night," Skinner said. "To be able to bring it every night and compete that hard for that long is probably the most unique thing about [Staal]."
Two of Skinner's 30-goal seasons came when he was Staal's teammate: his rookie season of 2010-11, when he scored 63 points (31 goals, 32 assists), and 2013-14, when he scored 54 points (33 goals, 21 assists).
"I hope last year was a bit of an anomaly for him," Staal said. "I think he's going to be counted on for a lot."