Brian Goodwin, A.J. Cole, Wilmer Difo, Matt Grace and Matt Skole are among the players eligible for Rule 5 draft protection.
Because of a full major league roster, the Nationals don't make a pick in the major league portion of the draft.
The Nationals must decide which players they will protect from the Rule 5 draft by Wednesday at midnight.
The Nationals opt not to pick any players in Thursday's Rule 5 draft and instead lose four, including speedster Kobernus and lefty Rosenbaum.