"Until we have something to announce, we're not going to discuss it openly in the press," Krivsky said from Sarasota, Fla., where the team is holding its annual organizational meetings.
Baker has a 1,162-1,041 career record with the Giants (1993-2002) and Cubs (2003-06), and is a three-time National League Manager of the Year winner.
An e-mail to Baker's agent, Greg Genske, was not returned.
The only other known candidate is interim manager Pete Mackanin, who took over the team from Jerry Narron on July 1 when Cincinnati was 31-51. Mackanin posted a 41-39 record and positioned himself as a leading contender for the permanent position.
Since Narron's dismissal, rumored candidates have also included former Marlins manager Joe Girardi and former Diamondbacks skipper Bob Brenly, who made his interest in the job known over the summer. Cardinals manager Tony La Russa's name also been a popular one as he mulls whether to return to St. Louis. Reds owner/CEO Bob Castellini was a former minority shareholder with the Cardinals.
Mackanin is at home in Bradenton, Fla., which is adjacent to Sarasota. But he has not participated in the club's meetings, which began on Thursday and run through Monday.
"They've got my reports on all the players. It's fine," Mackanin said.
"It shouldn't be read into one way or another," Krivsky said. "He's fully aware of the situation. He's a candidate. He did a great job for us."
Mackanin and Krivsky have not been in contact with each other since the season ended on Sept. 30.
"They will make their decision when they're ready," Mackanin said while playing a round of golf on Thursday. "I'm just waiting patiently, hoping for the best."
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.