Last week, Reds general manager Walt Jocketty revealed that there had been talks with Reyes' agent. This week at the Winter Meetings, baseball sources revealed that the two sides are still talking and the interest remains.
Reyes, who pitched for the Reds from 1998-2001, is also talking to a handful of other teams. Most of the teams involved are discussing two-year deals, it's been learned.
Indications are that Reyes is seeking something similar to the three-year, $12 million contract Damaso Marte signed with the Yankees last month.
Reyes, a Type B free agent, declined the Twins' offer of arbitration on Sunday. With Minnesota since 2006, the 31-year-old has been a primary left-handed reliever in the late innings.
Last season with Minnesota, Reyes was 3-0 with a 2.33 ERA in 75 appearances.
The Reds turned to the free-agent market for relief help last month after Jeremy Affeldt signed a two-year, $8 million contract with the Giants.
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.