LaRoche had a $10 million mutual option for 2013, while Burnett's option was for $3.5 million.
Assuming the two players don't reach a new contract with the Nationals before Saturday, they will hit the open market and be allowed to negotiate with all 30 teams.
Because the two players each declined their half of the contractual options, the buyouts do not get activated.
LaRoche would have been owed a $1 million buyout if he had picked up his half of the option but the Nationals had declined their half, while Burnett's buyout would have been $250,000 under the same circumstances.
Both LaRoche and Burnett will now look to procure multi-year deals. LaRoche could search for something in the three-year, $32-34 million range while Burnett might be able to find a three-year deal similar to the one left-hander Jeremy Affeldt landed from the Giants three years ago, which paid out $14 million.
The Washington Post first reported that LaRoche and Burnett declined their options.