(AP Photo/Ross D. Franklin)

If the Nationals do not sign a left-handed reliever off the free agent market, it will not be for lack of a broad search.

The latest name to add to the list of southpaws the Nationals have expressed interest in, a person familiar with the situation said, is Eric O’Flaherty, a dominant Braves reliever coming off elbow reconstruction surgery.

The Nationals have not yet given him an offer, but they have maintained dialogue with O’Flaherty, who has been one of the best relievers in baseball for the Nationals’ preeminent NL East rival. The Nationals are one of six teams to have shown interest in O’Flaherty.

O’Flaherty would come with nontrivial injury risk. Last May, O’Flaherty, who will turn 29 in February, underwent Tommy John surgery on his lefty elbow. In 2014, he would have to sit out until early-to-mid May.

Even if O’Flaherty will miss a month, his signing could represent great value. If not for surgery, O’Flaherty may well have drawn interest as a closer on the free agent market. Now, though, he is seeking only a one-year deal to re-established himself as a backend reliever.

Over the past four seasons, O’Flaherty has punched up a 1.68 ERA over 193 innings, averaging 54 appearances despite not pitching after May 17 in 2013. He steamrolled the Nationals, allowing them to hit .181 against him over his career. He faced the Nationals 21 times over the past three years and did not allow a single earned run.

O’Flaherty joins a long list of possible targets for the Nationals, whose need for a lefty reliever grew more start after they included Ian Krol in the package that acquired Doug Fister from Detroit.

The Nationals had dialogue with both Manny Parra and Javier Lopez before they re-signed with the Reds and Giants, respectfully. They have also shown interest in Boone Logan, Scott Downs, J.P. Howell and Oliver Perez, according to a people familiar with the situation. (The interest in Downs, whom the Braves traded for last year to replace O’Flaherty, was first reported by MLB.com.)

“We think that’s one of the things we have to address,” General Manager Mike Rizzo said Tuesday. “We have in-house options there. I think we’re better suited going into spring training with our left-handed bullpen than we did last year. But it’s something that we’re looking into the free agent market or the trade market and trying to upgrade. It’s a spot that we feel that we have to upgrade at. That said, I think we have some in-house options that can perform at a high level for us.”