Why should the Royals move quickly? After all, they have one of baseball's most-sought starting pitchers and, once left-hander Cliff Lee signs, the Royals hold the remaining ace.
The thing is, Moore wants a lot for Greinke, and he's not likely to move until he gets what he wants.
"I can give you examples -- I won't -- but there are examples that we've been close to dealing Zack or other players in the past if we get the right pieces included, and it just hasn't happened," Moore said.
So, unless some club suddenly comes up with an offer he can't refuse, and Moore concedes that's always possible, don't look for quick action.
Moore insists that the recent Greinke gold rush is different only because it's been much more public.
"The attention on Zack Greinke, believe it or not, is not any different than it's been in any offseason or prior to any Trade Deadline," Moore said. "It's the same group of teams that continue to inquire about Zack. The only difference between this year and years past is that Zack has commented from time to time about his particular future in Kansas City or has voiced an opinion about our baseball team."
Greinke, who last season expressed impatience with the Royals' rebuilding efforts, has two years left on a $38 million deal he signed prior to the 2009 season.
"Every Major League player has a very small window of opportunity to win. Zack's no different," Moore said. "Zack has felt this way about our Major League team since I've been here.
"He felt this way in 2008 ... he won 13, Gil Meche won 14, Mike Aviles was our Major League Player of the Year, Alex Gordon was set to break out, Billy Butler was getting better. We made some deals in the offseason to get Coco Crisp and Mike Jacobs and, all of sudden, he was excited about being here long term."
That's when Greinke agreed to his four-year deal.
Although Greinke has designated 15 clubs on his no-trade list, he could void that if it meant going to a contending team.
"We've got to work within the 15, but the fact that Zack wants to win would mean that he'd be open to evaluating every potential opportunity," Moore said.
The number of teams seriously hot on Greinke's trail varies, according to the latest rumors.
The Yankees apparently have determined that Greinke, with his history of a social anxiety disorder, would not be a good fit in the hot blast of media and fan scrutiny in Gotham. The Twins seemingly have veered away because the Royals want such a costly package.
The Rangers, pending what happens with keeping Lee, might be a fit, if willing to part with left-hander Derek Holland or prospects such as outfielder Engel Beltre or pitchers Martin Perez and Tanner Scheppers.
The Royals' search for a right-handed outfielder could involve Ryan Braun, but the Milwaukee Brewers like the five-year, $40.5 million package remaining on the slugger's contract, a relative bargain these days.
The Blue Jays have been sniffing around, but they're not likely to part with hot-shot pitcher Kyle Drabek to make it work. However, Jays watchers feel they might be willing to move along second baseman Brett Lawrie, just acquired on Monday from the Brewers. He's a strong right-handed hitter who could switch to the outfield.
Not surprisingly, free-agent outfielder Jeff Francoeur has been linked to the Royals. The 6-foot-5 right-handed batter had 13 homers, 65 RBIs and a .249 average in 139 games last year for the New York Mets and the Rangers. With the Atlanta Braves, Francoeur had 29 homers in 2006 and 105 RBIs the next season.
Moore, with the Braves when Francoeur was scouted and signed, commented only: "Yeah, he's a guy that you look at and I just don't want to comment, per se, on individual players."
Others who might draw interest include Melky Cabrera and Matt Diaz, both cut loose by the Braves, and Austin Kearns, a free agent from the Yankees.
Moore did say that no offers were out on any players, and he specified what he was looking for in an outfielder.
"We're going to have to get somebody," he said. "We want to look at guys that are still young, that have a lot of motivation, have had success in the past, potentially hungry, that need an opportunity to play every day to establish themselves ... guys that'll play from day one to day 162 and they'll give us an effort and an energy level that [manager Ned Yost] expects and our fans expect."
Francoeur is 26. The Royals are scanning the trade market, too.
"We have certain trade scenarios we're looking at that could potentially fortify our outfield, but nothing is imminent at this point," Moore said.
Not on that front or the Greinke front.