But Cora had not heard from the Brewers as of early Thursday afternoon, according to a source.
Cora was a finalist for the Seattle Mariners job before the Mariners hired Don Wakamatsu in 2009.
Cora spent parts of his 11-year playing career with the Mariners and White Sox, including joining Ozzie Guillen on the Sox's 1993 West Division championship team. He was on three playoff teams with Seattle and was an All-Star in 1997 with the Mariners.
After becoming the White Sox manager, Guillen brought Cora along as his third base coach and bench coach.
ESPNChicago.com baseball reporters Bruce Levine and Doug Padilla contributed to this report.