But there's a problem.
"It's a thin market. There's a reason we were able to move [Leo] Nunez and [Ramon] Ramirez for two everyday position players, because other people recognize the market's low," Moore said. "We knew that before we did that but, at the same time, we felt it was important to get two everyday players."
Nunez was traded to Florida for first baseman Mike Jacobs and Ramirez went to Boston for center fielder Coco Crisp. Now the Royals need someone to set up closer Joakim Soria.
"One of our strengths is Joakim Soria," Moore said. "We've got to get to Joakim Soria."
Remaining righty relievers on the Royals' 40-man roster include Robinson Tejeda, Joel Peralta and Carlos Rosa with Franquelis Osoria and Yasuhiko Yabuta as non-roster candidates.
"We need to add to that, from the right side. Left-handed we have some depth with [John] Bale, [Jimmy] Gobble, [Ron] Mahay and [Neal] Musser," Moore said. "We like the depth there, but from the right side we need to get better."
Trading for bullpen help is not the likely route.
"It's very difficult to trade for right now, so I'd look for it to come from the free-agent market," Moore said.
The Royals were to hear about two free-agent bullpen possibilities, Brandon Lyon and Kyle Farnsworth, from agent Barry Meister. Both are right-handers who could step in as setup men to replace the departed Ramon Ramirez and Leo Nunez.
Meister arrived at the Bellagio Hotel on Monday and plunged right into the Winter Meetings scene.
"Right now, I'm just meeting with clubs, and I'll try circling with Kansas City," Meister said. "I'm just really going through the market and talking to people now."
Lyon, 29, started last season as the Arizona Diamondbacks' closer and had 15 straight saves in one stretch. His effectiveness waned, however, and he lost the closer job. A statistical barometer: through July 18, opponents hit just .238 against him, but for the rest of the season the figure jumped to .392.
Final figures for Lyon included 26 saves in 31 chances, a 3-5 record and a 4.70 ERA in 61 games.
"Lyon is kind of a four-pitch guy. He closed with Arizona and we're talking about a premium reliever that can get you to the ninth inning and [we're] also looking for a closer's job," Meister said.
Farnsworth, 32, pitched most of last season for the New York Yankees and finished up back with the Detroit Tigers, traded for catcher Ivan Rodriguez. Combined for the two clubs, the power pitcher was 2-3 with a 4.48 ERA in 61 games.
The Royals have been sifting through other relievers, too, including Juan Cruz, 30, who was 4-0 with a 2.61 ERA in 57 games for the Diamondbacks.
"He's had a great year, a great two years really. We'll see," Moore said.
Last season Cruz was third among Major League relievers with 12.37 strikeouts per nine innings, getting 71 strikeouts in 51 2/3 innings. For a righty, he was very effective against left-handed batters, holding them to a .159 average as opposed to .221 by right-handed batters.
After coming off the disabled list with a strained oblique, Cruz zoomed through his last 20 appearances with a 1.71 ERA.
The Royals also were looking at Russ Springer, 40, who was impressive the past two seasons with the St. Louis Cardinals. Springer was 8-1 with a 2.18 ERA in 76 games in 2007 and 2-1 with a 2.32 ERA in 70 games last season.
"We'll figure out how to put the bullpen together somehow, some way through the efforts of our scouts and [pitching coach] Bob McClure's magic," Moore said.
Meantime, there were a couple of other items on Moore's agenda.
"We'd like to add another starting pitcher. I don't know if we can. We'd like to add a middle infielder. I don't know if we can," he said.
Meister suggested his client Craig Counsell, a free agent from the Milwaukee Brewers, as an infield possibility but the Royals didn't seem interested.