Abdullah suffered a season-ending foot injury in September but is fully recovered and is expected to be available throughout the summer.
Asked if Abdullah will be the starter, Quinn responded "He is," according to ESPN's Michael Rothstein.
Abdullah leads a running backs group that includes Zach Zenner, Theo Riddick, Dwayne Washington, and Mike James.
The 23-year-old rushed for 597 yards and two touchdowns during the 2015 season, playing in all 16 games.
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