Valdez and Ramirez had opt outs in their contracts with the team, Andrew Baggarly of CSNBayArea reports (Twitter links). The Giants would like to re-sign Ramirez to a minor league deal if he doesn't find a better opportunity elsewhere.
Valdez, a client of Wasserman Media Group, appeared in 77 games for the Reds in 2012, playing shortstop, second base, third base and even center field. The 34-year-old posted a .206/.236/.227 batting line in 208 plate appearances with Cincinnati.
The Giants signed Ramirez to a minor league deal last month. He appeared in 58 games for the Mets in 2012, posting a 4.24 ERA with 7.4 K/9 and 4.9 BB/9 in 63 2/3 innings out of the bullpen. The 31-year-old had a 46.7% ground ball rate and his fastball averaged 91.1 mph, according to FanGraphs.