Ken Rosenthal of Fox Sports reports that Valverde is uniform at the Nationals spring training complex.
Valverde has not pitched in the majors since being released by the Mets in May 2014. He accumulated a 5.66 ERA with 23 strikeouts in 20 2/3 innings with New York prior to his release.
The 37-year-old signed a minor league deal with the San Diego Padres in January but was released earlier this month.
In his last full season in the majors in 2012, Valverde had a 3.78 ERA in 69 innings for the Detroit Tigers, striking out 48 and saving 35 games. In 2011, he led MLB in saves with 49.
According to The Washington Post, Washington has already used 11 relievers this season and four Nationals pitchers have made their major league debut in the last two weeks.
The Nationals (8–13) play the Braves (10–10) in Atlanta on Wednesday night.
- Molly Geary