Renteria, 51, managed four seasons in the Padres' Minor League system before joining the big league staff as a first-base coach in 2008, and he was promoted to bench coach in 2011. He also managed Mexico's team in the 2013 World Baseball Classic. He played parts of five seasons with the Pirates, Mariners and Marlins, and he has also managed in the Marlins' organization.
Renteria, who had a phone interview with the Blue Jays for their opening in 2011, was asked by MLB.com in March if he thought he would get the chance to be a Major League manager.
"I'll say the same thing I always say: Those things kind of take care of themselves. I don't think of it too much. I think what's most important is the job I'm doing now, and that's the job that I need to be focused on.
"Those other things, I've never worried about that. I've been fortunate to be here with a great coaching staff."
Martinez, 49, has served as the Rays' bench coach since 2008. He was Chicago's third-round pick in the 1983 Draft and reached the Majors with the Cubs in 1986 before being traded during the 1988 season. He returned to the North Side in 2000 and played 18 games for the Cubs.
Martinez played a total of 16 years in the Majors with the Cubs, Expos, Reds, Giants, White Sox, Devil Rays, Rangers, Blue Jays and Braves.
"I'm very excited to have this opportunity," Martinez said. "Getting this job would be awesome. It's where I started my whole career. [Wrigley Field] is probably the best field I've ever played on."
Other candidates who have already been interviewed to manage the Cubs include former Nationals and Indians manager Manny Acta and former D-backs manager A.J. Hinch.
Epstein has said he would like to have a new manager in place by Nov. 11, when the General Manager eetings begin.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.