Martinez, 49, will fly to Chicago this week to interview for the post.
"Getting this job would be awesome," Martinez said. "It's where I started my whole career. [Wrigley Field] is probably the best field I've ever played on."
Martinez has been the Rays' bench coach since 2008. He made his Major League debut as a player for the Cubs in 1986 and spent his first three seasons in Chicago.
He has interviewed for managing jobs in Toronto, Cleveland and Houston in the past. Martinez said he learned a little something from each of those interviews and has continued to learn in his role as the Rays bench coach under manager Joe Maddon.
An original Devil Ray, Martinez played 16 seasons in the Majors with eight different teams.
On Monday, the Cubs interviewed Padres bench coach Rick Renteria for the position, after already interviewing former Nationals and Indians manager Manny Acta and former D-backs manager A.J. Hinch.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.