"I'm not saying it's beyond the realm of possibility, but I think right now it's better to keep him in that ninth-inning role," Wedge said. "But I think in the future he can be a one-plus guy."
Though League has appeared in 285 Major League games in relief, he is still new to closing consistently, with a career-high 26 saves this season.
"One-plus [innings] is a big difference [from] just getting those last three outs," Wedge said. "It's tough enough to get those last three outs, but to ask him to come in in the middle of a situation in the eighth inning, then sit back down and go back out there and run through the ninth inning, it's a significant step."
League has pitched in 47 games this season, finishing 43, and has recorded more than three outs only once, getting four in a loss on May 8.