Alex Brandon / AP

General Manager Mike Rizzo said he likes where the Nationals’ bullpen stands heading into the winter, but he wants to upgrade the left-handed portion of his relief corps. That makes sense, because as he acknowledged, the Nationals currently have no lefty relievers under contract – Tom Gorzelanny is eligible for arbitration, and both Michael Gonzalez and Sean Burnett are free agents.

The Nationals have been in touch with both Burnett and Gonzalez, and “I would like to bring back both of them,” Rizzo said. If they cannot, then finding an alternative – perhaps free agent Jeremy Affeldt? – would become a bullpen priority.

Rizzo seemed disinclined to tinker with the back-end combination of Drew Storen and Tyler Clippard, both of whom are due for raises in arbitration. He also included Craig Stammen and Ryan Mattheus as right-handed, power arms capable of heavy lifting. But he did not rule out searching for upgrades, either.

“If we have a chance to upgrade with an impactful arm, we certainly would consider it if it fits us,” Rizzo said. “I don’t know. It’s going to depend on what it costs and what type of performer he is. We feel good with the back end of the games. We feel really good with the seventh, eighth and ninth inning as is.”

Rizzo met Thursday afternoon with Scott Boras, who represents several free agents the Nationals could have interest in, including center fielder Michael Bourn, right-handed starter Kyle Lohse and, pertinent to the bullpen, closer Ryan Madson.

Madson missed the entire 2012 season after he tore his ulnar collateral ligament in spring training and underwent Tommy John surgery. He saved 32 games in 34 chances for the Phillies in 2011, and his experience would give the Nationals an added dimension to go with Storen and Clippard in the back end. Over his previous five full seasons, Madson punched up a 2.89 ERA with 8.6 strikeouts per nine innings.

“I think they have an opportunity this offseason to build their bullpen,” Boras said. “I think they have an opportunity to really create some strengths where there were weaknesses, because the free agent market allows them to do that. The perception of the Washington Nationals, the revenues, it’s a great thing for the game.”

The Nationals could upgrade in their bullpen internally with a healthy Henry Rodriguez. The flame-throwing right-hander missed the final two-thirds of the season with a bone spur in his right elbow. Rizzo said the injury led to inconsistencies when Rodriguez posted a 5.83 ERA and lost his grip on the closer’s job.

“He’s doing well,” Rizzo said. “He’s successfully rehabbing. He said he’s right on pace. He said he feels terrific, better than he has in a long time. Who knows how long he had that bone chip in there?”

Rodirguez’s healthy return would give the Nationals a bevy of options. For right-handers, assuming they do not trade either Storen or Clippard, they would have Storen, Mattheus, Stammen, Clippard, Rodriguez and, if his conversion to starting doesn’t stick, Christian Garcia. They still control Gorzelanny’s rights, and they will need at least one other lefty.

The Nationals’ bullpen is like the team as a whole: It’s set up to be strong next season, and they have a lot of options in choosing how to maximize it.

A couple other nuggets from the day at the GM Meetings:

>>> Not surprisingly, Rizzo expects first baseman Adam LaRoche to decline his one-year, $13.3 million qualifying offer before the 5 p.m. Friday deadline. If LaRoche indeed declines and signs with another team, the Nationals would receive a compensatory draft choice.

>>> The Nationals do not plan to be aggressive this winter in pursuing contract extensions for young, core players entering arbitration like shortstop Ian Desmond or starters Ross Detwiler and Jordan Zimmermann. The Nationals broached an extension with Zimmermann early in the 2012 season, but the talks never moved into an advanced stage.

“Those deals, those are our core players,” Rizzo said. “We control those guys. Those decisions make sense if they make sense both ways. With the security of extensions comes risk with the team. I feel when we’re adding the risk, it has to make sense for you financially to do it.”