Quinn and Anderson participated in this week's voluntary minicamp, which started Tuesday and ends Thursday.
Mangini said he is being balanced with the reps of his quarterbacks, but Quinn's performance so far this offseason has helped him earn an early advantage over Anderson.
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Brady Quinn throws his first career TD to Kellen Winslow.
"Brady will get the first reps today," Mangini said. "He started with the first reps on Wednesday, and that's because he's done a really outstanding job in the offseason program. Not that Derek hasn't done well, but [Quinn] gets the first reps."
Quinn and Anderson have been together with the Browns since 2007, but this is the first time both players have competed actively for the starting job.
Quinn became Cleveland's first-round pick out of Notre Dame in 2007, but a lengthy contract holdout opened the door for Anderson to win the job and have a Pro Bowl season.
Quinn finally saw his first action in 2008 after Anderson struggled. But Quinn was inconsistent in three starts before suffering a season-ending finger injury.
The Browns also traded for former New York Jets quarterback Brett Ratliff in April. But Mangini said his focus this offseason is on Quinn and Anderson competing for the starting job.
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Josh Cribbs of Cleveland Browns shows for team meeting, but does not practice
