NASHVILLE, Tenn. -- The center-fielder market is dwindling.

But Phillies general manager Ruben Amaro Jr. insisted Tuesday he does not feel backed into a corner at the Opryland Resort & Convention Center, site of the Winter Meetings. B.J. Upton, Angel Pagan and Shane Victorino have either signed contracts or agreed to terms with the Braves, Giants and Red Sox, respectively. The Nationals acquired Denard Span from the Twins.

That leaves free-agent center fielders Michael Bourn and Josh Hamilton still available, and there are reports Hamilton is close to re-signing with the Rangers.

If Amaro is frustrated, he tried not to show it.

"It was a pretty encouraging day, because there are some possibilities out there that I like," Amaro said inside the team's hotel suite. "But just like in any other situation, there are ebbs and flows. One day you think you have a deal done, and 30 minutes later it's off. When you say, 'Are you close to something?' 'close' doesn't mean [anything]."

It remains to be seen if the Phils can cross the finish line on any of the possibilities Amaro said he likes, but he made a specific point to crush one rumor floating through the lobbies and hallways of the sprawling hotel. There had been a report the Phillies and D-backs had engaged in discussions about a Cliff Lee-for-Justin Upton swap, with Philadelphia including millions of dollars in the deal.

"That would be incorrect and false," said Amaro, who normally does not comment on trade rumors. "I don't know where that would come from, but as you all well know, there are a lot of falsehoods out there, and that is absolutely one of them."

It seems to make little sense to trade Lee, especially if it means Philadelphia would have to chip in money to complete the deal. The club needs Lee in the rotation, considering Roy Halladay is trying to rebound from a mediocre year.

"I think our best chances are to keep the core together," said Amaro when asked if he would trade a key player or two to fill needs. "Our best chance to win is to keep the core together and healthy. So probably not. Probably not move any of the core players on our club, because I think it would just weaken us too much. I don't think we'd get the value that we would need if we moved any of those guys to make us a better club necessarily."

Lee also has a limited no-trade provision, and the D-backs are not on his list of approved teams.

But the idea the Phillies need to trade pitching to acquire a center fielder, corner outfielder or third baseman is accurate. The Phils have pitching and catching depth in the organization. CSNPhilly.com reported Philadelphia is dangling right-hander Vance Worley and would include right-handed prospect Trevor May in the right deal.

That would seem to be the price for a quality bat at this point. Amaro has pulled the trigger in the past when it comes to dealing prospects, and as much as he says he hates it, he might have no choice.

Amaro said there are a couple prospects he would consider untouchable, but "not a lot of them."

"I'm trying to keep all of the young players we possibly can," Amaro said. "We have surplus in other areas that people are interested in, rather than moving top-level prospects. We're going to try to keep as much young talent as we can. ... It seems like the price of doing business is getting higher and higher. It makes you concentrate on developing your own players. I think there are still valuable players out there to be had, and that would fit in what we're trying to do."

The Phillies like free-agent corner outfielder Cody Ross. They have talked with Ichiro Suzuki. FOXSports.com reported the Phils have interest in Scott Hairston, a player they have looked at in the past. If Philadelphia wants to get creative, it could look to acquire a corner outfielder and third baseman or two corner outfielders and sign somebody to a one-year deal to play center field. FOXSports.com also reported Nate McLouth is only looking to sign a one-year deal because he believes he can reestablish his market next offseason. That could be a low-risk move.

Asked if the Phillies need to acquire a center fielder before they do anything else, Amaro said no.

That makes sense. There aren't many left.

Bourn remains available. Amaro said he had not met with his agent Scott Boras, "but I wouldn't tell you if I did."

So the Phils are keeping quiet publicly. But they have been quiet privately, too. They hope that changes soon.

Extra bases

• The Phillies still need a setup man. "It's a priority. It's not a necessity," Amaro said. "I'd very much like to have a veteran arm, but it's like a lot of these other folks. They're being valued very high."

• Amaro said the Phils have some interest in some guys available in the Rule 5 Draft. In recent seasons, the Rule 5 Draft helped them acquire Victorino, David Herndon and Michael Martinez.