Parker averaged 8.3 points in 72 games last season. The 36-year-old veteran is a candidate to be Cleveland's starting shooting guard. Parker originally signed with the Cavaliers prior to the 2009 season.
"From the beginning, Cleveland was the team that showed the most interest," he said. "That's a good indicator of where you fit in with an organization and how they plan to use you."
Omri Casspi injured his left knee at practice on Sunday and is expected to be sidelined for a couple of days.
Also Monday, Cleveland officially introduced rookie guard Kyrie Irving, 19, the No. 1 pick in the draft, as well, on a busy day at camp.
Asked what he thought of Irving after watching him practice for three days, Cleveland coach Byron Scott smiled and said, "He's pretty good. The one thing about Kyrie is each day he shows you a little something special. The first day it might have been one thing. Then we had a scrimmage and there were five or six things. He's progressing very nicely."
The Cavaliers, who were 19-63 last season, open the preseason Friday against Detroit. The teams play again on Dec. 20. Cleveland opens the regular season against Toronto on Dec. 26. Davis' absence, whether it's temporary or permanent, will speed up Irving's progress.
"If Baron isn't here or not playing in the preseason games or when the regular season starts, it obviously gives him (Irving) more responsibility," Scott said. "But I'm still not quite sure I'm just going to hand him the ball."
Irving is pleased with the way his first professional camp is going.
"I'm trying to learn as much as possible and get used to the pace of the game," he said. "It's a little different knowing they expect a lot more at this level."
Irving realizes he must adjust quickly since the season begins in less than two weeks.
"It's a quick turnaround," he said. "That's something I have to get used to. In college, you get a grace period. Right now, you have a week of training camp, you play your preseason games and you play the first game in practically a week and a half."
Grant said the Cavaliers have received an extension on the trade exception they received when LeBron James went to Miami. The team has until Friday to use it, but Grant said there is no urgency to do so. ... The Cavaliers will explore other free-agent possibilities, but Grant thinks the team is in a good spot with the current roster. ... C Semih Erden has yet to take part in basketball drills because of a thumb injury. Scott said he should be able to participate in a full practice in early January. ... The Cavaliers waived free-agent F J.P. Prince.
Information from The Associated Press was used in this report.