Zach Duke (Katherine Frey / The Washington Post)

The Nationals have only one left-handed reliever signed for next season, and that’s Zach Duke, who agreed to a one-year deal on Monday. But, despite the Nationals’ right-handed relievers’ success against left-handed batters, Manager Davey Johnson would still like to add another southpaw to the bullpen.

Johnson gave the clearest sign yet that left-hander Sean Burnett is likely to agree to a deal with another team, and that the Nationals haven’t ruled out bring back veteran lefty free agent Michael Gonzalez or non-tendered lefty reliever Tom Gorzelanny. 

Left-handed relievers are in high demand this offseason, and will command a high price. As of Monday, Burnett was out of the Nationals’ desired range in terms of price and years, according to General Manager Mike Rizzo. Burnett could receive a contract similar to the three-year, $18 million deal that fellow lefty Jeremy Affeldt signed with the San Francisco Giants last month.

“I’ll miss Sean Burnett,” Johnson said. “He’s probably going to go somewhere else.”

Nationals right-handed relievers such as Tyler Clippard and Craig Stammen are particularly effective against left-handed hitters, and could be options should the team not reach a deal with a left-hander. Clippard held left-handers to a .170 average last season in large part because of his change-up, while Stammen, with a power sinker and slider, allowed them to hit only .198 off him.

“I would like another left‑hander out there,” he said. “I just like to have some decisions to make once in a while. But I would like the balance because we’re pretty much going to have five right handers in the bullpen and only two lefties out there with them. I like where we’re at.  Like I say, I don’t have much of a wish list.  We can figure it out with what we’ve got.”

Gonzalez, who hopes to reach a deal with a team this week and expressed interest in returning to Washington earlier this winter but sought a multi-year deal, was effective last season, posting a 3.03 ERA in 35 2/3 innings and holding lefties to a .179 average. Gorzelanny, who the Nationals are open to bring back for a cheaper deal, posted a 2.88 ERA over 72 innings in a variety of roles and held lefties to a .237 average.

One name to keep in mind will be free agent J.P Howell, who spent the past seven years with the Tampa Bay Rays and posted a 3.04 ERA in 50 1/3 innings last season.

“There’s a lot of them out there,” Johnson said. “Michael Gonzalez did a good job for us, and I love Gorzelanny. I like taking money from him on the golf course, too, on the off days, and he kind of fits.”

“We had a great core out there that got along very well and helped each other not only on the field but off the field,” Johnson added. “And you don’t want to mess that, mess with that mix too much. So hopefully, we’ll get one of those guys who were with us last year.”

Duke, right-handers Stammen and Christian Garcia, who will compete as a starter in spring training, will also provide starting depth should anything happen to the starting pitchers. Whether Garcia, a September call-up who impressed all with his stuff, remains as a reliever or starter, Johnson said, still remains to be seen — though a starting spot seems unlikely given the Nationals agreed to terms with free agent starter Dan Haren on Tuesday morning.

“The players make the decisions, just by their performance,” Johnson said. “I never even worry about it. I just set it up and go through the spring, and it will be at the end of spring, everybody will know the answer. So I’m not making any judgments that he’s going to be in the rotation, but that’s what I’m going to give him every opportunity to do.”