LaRoche, who earned Gold Glove and Silver Slugger Award honors recently while hitting .271 with 33 home runs and 100 RBIs, is the top first baseman on the free-agent market.
LaRoche, 33, turned down the Nationals' one-year, $13.3 million offer -- the average of the previous year's top 125 salaries. The Nationals receive a compensation pick between the first and second round of the 2013 Draft should LaRoche sign with another team.
The signing team would give up its first-round selection, though the top 10 picks of the Draft are protected, so any team holding a top-10 pick forfeits its second-round selection if it signs a player who received a qualifying offer.
A baseball source familiar with the Nationals and LaRoche said the two parties haven't talked in a few days, but indicated that LaRoche would love to return to the Nationals. LaRoche is looking for a multiyear deal.
If LaRoche goes elsewhere, the Nationals most likely will move Michael Morse back to first base and look for a left-handed-hitting slugger.
A nine-year veteran, LaRoche has hit .269 with 197 home runs and 684 RBIs during his career with the Braves, Pirates, Red Sox, D-backs and Nationals.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. Bill Ladson is a reporter for MLB.com and writes an MLBlog, All Nats All the time. He also can be found on Twitter @WashingNats. This story was not subject to the approval of Major League Baseball or its clubs.