According to the Washington Post, LaRoche is in negotiations with "multiple" opposing clubs. Reports surfaced earlier in the week that the Boston Red Sox are interested in LaRoche in case Boston can't restructure a deal with free agent Mike Napoli.
Still, the club could re-sign LaRoche, and then opt to trade Morse to help the club in other areas.
LaRoche enjoyed one of the best years of his career in 2012, batting .271/.343/.510 with 33 home runs and 100 runs batted in.
It is believed that LaRoche is seeking a three-year deal, but the Nationals are reluctant to give the 33-year-old first baseman a three-year contract.