(Jeff Roberson/AP)

In early May, the Nationals made a seemingly minor move, signing veteran left-handed reliever Michael Gonzalez to a one-year minor league deal. A month later, Gonzalez was added to the roster and soon became a valuable presence in the bullpen, an effective and well-liked left-handed reliever with postseason experience who pitched important innings down the stretch.

And now, the 34-year-old free agent reliever wants to return to Washington, an idea he said the Nationals are open to.

“They’ve had a couple conversations,” Gonzalez said in a telephone interview Saturday morning. “[My agent] told me that they’re definitely interested and I’m definitely interested. It’s going to be good. We haven’t started throwing money there. But there’s interest on every side.”

One of the Nationals’ priorities this offseason will be the need to beef up their bullpen. The Nationals’ top two left-handers, Sean Burnett and Gonzalez, are both free agents. If they lose Burnett because he is a hot commodity on the open market, Gonzalez could still provide the effective left-handed arm out of the bullpen. In a division where the rival Braves have a left-handed heavy lineup, Gonzalez seems like a logical fit. Left-handed batters hit .179 off him last season.

Gonzalez, a 10-year major league veteran, proved to be one of General Manager Mike Rizzo’s most unheralded moves this season. Rizzo had scouted Gonzalez, a former closer, during his stints with the Pirates and Braves. Gonzalez pitched 35 2/3 innings, striking out 39 batters and posting a 3.03 ERA for the Nationals this season, after only joining the team in early June. Fellow left-handers like Ross Detwiler credited Gonzalez, who pitched in the World Series for the Texas Rangers in 2011, with helping him develop this season.

Gonzalez’s strong season in Washington could earn him the multi-year deal he is seeking. While it may be tough to secure one at his age, good bullpen arms are in demand and plenty of teams could use a reliever of Gonzalez’s stature. He said that about 10 teams have shown interest in him this offseason. Before signing with the Nationals last season, Gonzalez said he spurned interest from the Yankees, Red Sox and Reds but settled on Washington because he felt it was his best chance at winning.

“You’re always shooting for a two-year deal,” he said. “The guarantee, the security. I’m at the point in my career where I’m going to the team I feel comfortable most.”

Gonzalez was previously represented by super agent Scott Boras but dropped him and returned to Dan Lozano of MVP Sports Group, who has represented him in the past. Gonzalez said he would be open to hearing from other teams, but his top priority now is staying with the Nationals.

“Brother, it was ridiculous,” he said of the season. “From the management to the players, it was first class. I had a great time with the guys. The camaraderie was awesome. And the pitching, everyone is coming back. I still feel like we’re going to have the best rotation in the league. And I think we have the chance to repeat what happened last year. … I had a great time. The city, the fans. It was just a different scene.”