Quinn, who figures to compete for the starting job with Charlie Frye and Derek Anderson, has missed six practices so far.
Browns general manager Phil Savage has been in negotiations with Quinn's agent, Tom Condon, but the team said there was nothing new to report.
"I'm glad we've got the other guys out there," Savage said. "If anything, it's given Charlie and Derek the chance to get more reps, and that's a positive."
Savage characterized talks with Condon as "in the same neighborhood, but not on the same street."
With the exception of Quinn, all of Condon's picks in the first two rounds are in their respective camps.
Quinn also missed the club's rookie orientation program last week. Frye understands the importance of getting to camp as soon as possible.
"You just want to get here and build relationships with guys," Frye said. "This is the hardest part of the season, being in training camp. You just got to be optimistic and when you get here, you got to learn fast."