There are no plans, Jocketty said, to explore adding any left-handed relievers to the bullpen from outside the organization. Besides Chapman and Willis, the Reds already have lefties Bill Bray, Matt Maloney and Daniel Ray Herrera at their disposal as potential candidates.
With the holidays now in the rear-view mirror, the Reds' offseason should heat up if last year's activity is any indication. Jocketty waited out the market as winter moved along and improved the club with late additions like Orlando Cabrera and Miguel Cairo, the re-signing of Jonny Gomes and the winning bid for Chapman.
"We're still looking for a veteran infielder that can play shortstop and second base," Jocketty said. "And we're looking for a veteran outfielder, preferably a left-handed hitter for the bench."
Rhodes signed with Texas for $3.9 million in 2011 and has a vesting option worth $4 million in 2012. The Reds weren't willing to add the vesting option to the deal and let the 41-year-old walk. Some of the money that would have been allocated to Rhodes could now be diverted toward the other additions the Reds are seeking.
For the infielder, the club has interest in veteran shortstop Edgar Renteria.
"We've been talking with them and a couple of other people," Jocketty said. "Whoever we sign will be more of a complementary player that's able to play different positions and bring experience."
Renteria's agent, Barry Meister, would not go into detail about his client's interest in the Reds.
"We're not close to a deal with anyone on Edgar," Meister said. "Edgar knows Walt from their days in St. Louis, and we have great respect for him."
A member of three World Series teams, including the champion Giants last season, Renteria batted .276 in 72 games.
There are no plans to displace Paul Janish from having the inside track for the starting shortstop spot.
As for the outfielders, the left-handed hitter being sought could also double as a potential leadoff hitter. There have been talks, Jocketty confirmed, with the agents for Scott Podsednik and Fred Lewis -- both are left-handed and speedy.
Podsednik, 35, batted .297 with a .342 on-base percentage and 35 steals with the Royals and Dodgers last season. He was caught stealing 15 times. With the Blue Jays in 2010, the 30-year-old Lewis batted .262 with a .332 on-base percentage and 17 steals.
There hasn't been very much movement in talks with any of the Reds' arbitration-eligible players, namely National League MVP Joey Votto.
"We really haven't done much around the holidays. We haven't had any real discussions," Jocketty said.
Jocketty was just learning about the reports that Rockies outfielder Carlos Gonzalez agreed to a seven-year, $80 million contract. Gonzalez finished third in the NL MVP race this fall, and his signing could affect the number that Votto reaches. However, Gonzalez is still a year away from arbitration eligibility and less established than Votto after his first season in Colorado.