Several of the organization's top prospects were cut from major league camp.
The right-hander is scheduled to throw a Friday bullpen session, his first since his elbow discomfort first appeared.
Major league camp is down to 49 players now.
Third baseman says he would play if it were the regular season.
Rivero is optioned to Class AA Harrisburg and Cole is reassigned to minor league camp.
The right-handed starter played catch on Tuesday morning for the first time since feeling tightness in his elbow.
The veteran left-handed reliever said he chose the Nationals over four other teams because he felt comfortable with Washington.
Tanner Roark will make replacement start Friday against the Houston Astros in Viera.
The Nationals right fielder has a similar offensive philosophy to the new manager. Also, an update on his minor right bicep strain.
The towering right-hander will take the mound on Sunday in Viera against the Marlins.