Also, the Nationals are among the teams that have inquired about free agent infielder Asdrubal Cabrera.
Fister is a cheaper extension candidate than Jordan Zimmermann, but no talks have occurred since the last offer in spring.
The left-hander still views himself as a starter and it's unclear what the Nationals will do with him next season.
A New York Supreme Court judge will grant or deny MASN's discovery request on Dec. 15.
Zimmerman says his right hamstring strain has fully recovered and likes the Nationals' chances of contending in 2015 with the roster as is.
The Nationals split over $2 million into 58 full shares, each worth over $29,400.
Strasburg was in Washington over the weekend promoting a store opening.
A fixture at first base the past four seasons with the Nationals, the 35-year-old LaRoche heads to Chicago on two-year deal.
Billings and Stephen Strasburg were teammates at San Diego State University in 2007.
The Nationals don't have a need for a starter -- but two of them, Doug Fister and Jordan Zimmermann, are a year away from free agency.