Other than to say he was interested in the position, Price declined to comment further when reached by MLB.com. No interviews are believed to have been set.
"We are not going to rush into anything," Jocketty said on Tuesday. "We probably won't do anything until after the World Series. I'm not going to rush just to get it over with."
Two other anticipated candidates -- Triple-A Louisville skipper Jim Riggleman and Cubs third-base coach David Bell -- have yet to be contacted by the Reds. Jocketty identified Riggleman as an internal candidate on Friday.
Riggleman would also be interested in the position, if offered the opportunity.
"I haven't talked to anybody from the Reds," Riggleman said from his home in Florida. "All I know is what I've read on my computer about various names and jobs and who might be going where. At this time, it's par for the course. I'm sure the Reds will have a great list of candidates and a lot of people who want to manage there. I'm sure they'll get it settled in due time.
"If I am on the list, it would be flattering in itself. I would look forward to talking to them."
Riggleman, 60, is a former manager of the Padres, Cubs, Mariners and Nationals over 12 seasons. He resigned from Washington during the 2011 season due to a contract dispute.
This season, Riggleman managed his first year at Louisville after a 2012 season at the organization's Double-A Pensacola affiliate.
"In my two years with the Reds, Pensacola was outstanding and Louisville was outstanding," Riggleman said. "Both are great places for the Reds to have Minor League teams. I've enjoyed it a great deal. We'll be looking forward to coming back to Louisville if that's what happens."
As for Bell, he just completed his first season as the Cubs' third-base coach. When manager Dale Sveum was dismissed last week, his coaching staff was given the chance to pursue other opportunities. Other than to say he hadn't heard from the Reds, Bell declined to comment because he remains under contract with Chicago through the end of the month.
Bell, 41, managed for the Reds at the Double-A level from 2009-11 and at Louisville in 2012 before leaving for the Cubs' job. He was believed to have left the Reds on good terms.
As a player from 1995-2006 with six Major League teams, Bell batted .257 with 123 home runs and 589 RBIs. A Cincinnati native and Moeller High School alum, he is the son of former Reds player Buddy Bell and grandson of Reds great Gus Bell.
Jocketty is heading to Arizona soon to watch the Reds organization holds its final week of instructional league and to watch his players in the Arizona Fall League.
In the meantime, the process of finding a new manager will continue. The list of candidates is something Jocketty did not plan on making public.
"It's not fair to those who do not get the job," Jocketty said. "I don't want to have a large list and call a lot of people and get their hopes up. We will do a lot of due diligence."