Pettine could decide between Johnny Manziel, Brian Hoyer by Tuesday
"That should be the target date,'' Pettine said. "Something unforeseen could come up, but we're hopeful. I want to see if I can cut the quarterback questions down by about 90 percent after next week -- and the chemistry, continuity, it's important to establish that.''
Pettine also said he was unsure if he would make a "permanent commitment" to either quarterback.
"Quarterback is different from other positions, in that you do want to make a commitment,'' he said. "(But) I don't know if you can necessarily make a permanent commitment. So much can change over the course of an NFL season, the circumstances.
"But I think that's the one position where you probably have to have a little bit more patience, maybe than some others as far as if a guy's not performing to the level you think he can and you're not getting the results, then you'd go ahead and make a move. It's somewhere in between. I don't want whoever the starter is to feel like, 'oh, if I make one mistake, I'm out.' but I also don't want him to feel like, 'hey, I've achieved something, this is my team for the year.'''
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On Friday, Pettine addressed Manziel's chances of winning the starting job.
"Sure he can,'' said Pettine. "All of our options are still on the table. I think a lot of people read into what happened, but every option for us is still on the table.''
Hoyer completed 6 of 14 pass attempts for 92 yards in Saturday night's preseason opener against Detroit, while Manziel went 7-of-11 for 63 yards and added 27 yards on the ground.
On Sunday, Pettine denied a ESPN report saying that Manziel has moved ahead of Hoyer on the depth chart and said there was no front-runner to start the team's Sept. 7 regular-season opener at Pittsburgh.
"To me, if there was a clear-cut favorite at this point, it would probably mean that one of them wasn't playing very well,'' Pettine said. "And it's a good problem, having two guys that we think are both capable of being NFL starters.''
Hoyer, 28, threw for 615 yards, five touchdowns and three interceptions in three starts with the Browns last season before tearing his ACL. He went 3-0 in those games.
Cleveland selected Manziel with the No. 22 pick in this year's draft. The 21-year-old won the Heisman Trophy in his redshirt freshman season at Texas A&M in 2012.
The Browns went 4-12 and finished in last place in the AFC North last season.