Enroth, who turns 25 on June 25, helped Sweden capture the gold medal at this year's World Hockey Championship, and was named the tournament's top goaltender.
"I've been growing a lot," he said. "I want to play more. My goal is to be a starter one year in the NHL, and right now Ryan is the starter here. It's kind of hard to take the job from him here, but we'll see what happens."
The Sabres entertained trade offers for Miller this season, and are expected to continue those discussions this off-season and closer to the June 30 NHL Draft.
Many within the hockey community believe the Sabres will trade Miller this summer.
"I feel pretty comfortable when I get back-to-back starts and stuff like that, so I think I'm ready," Enroth told the News. "I learned a lot from this season, and from last season, too. You always learn from experience, and I'm just trying to build on this season for next year."
Enroth made $725,000 this season (his salary cap hit was $675,000), and is scheduled to become a restricted free agent July 5.
Sabres GM Darcy Regier has every intention of locking Enroth up to a long-term contract and the two sides will continue their discussions over the next month.