The closer for the Athletics last year, Balfour, 36, posted 38 saves with a 2.59 ERA in 65 games. If he joined the Nats, he would likely be a setup man.
Washington's roster is currently at the 40-man limit. If the Nationals were to sign Balfour, they would have trade a player or designate someone for assignment.
A baseball source indicated that reliever Drew Storen would likely be available if Balfour signs with the Nats. Storen, who struggled in the 2012 National League Division Series against the Cardinals, lost his closer's job after the team signed free agent Rafael Soriano to a two-year deal last January.
The role change appeared to affect Storen on the mound, as his struggles led to the righty being sent to Triple-A Syracuse for a couple of weeks. After he returned, Storen had a 1.40 ERA in 21 games.
In other news, the Nationals are still trying to improve their bench. They are still looking for a backup catcher, according to a baseball source. The club will most likely trade for that piece. Washington had interest in free agents Jose Molina and John Buck, but they signed with the Rays and Mariners, respectively.
The Nats currently have three catchers -- Chris Snyder, Sandy Leon and Jhonatan Solano -- on their Spring Training roster vying to be Wilson Ramos' understudy.
Bill Ladson is a reporter for MLB.com and
writes an MLBlog, All Nats All the time. He also could be found on Twitter @WashingNats. This story was not subject to the approval of Major League Baseball or its clubs.