The Nationals were among LeMahieu's suitors two years ago when he ultimately signed with the New York Yankees.
LeMahieu, 32, is the reigning AL batting champion after hitting .364 with 10 home runs in 50 games this summer. He's the first player in the modern era to win batting titles in both leagues.
The Nationals are hardly alone in their pursuit of the versatile All-Star, but LeMahieu's preference is believed to be a reunion with the Yankees. The Toronto Blue Jays and New York Mets are also reportedly in the mix.
Starlin Castro is currently projected to be the Nationals' starting second baseman, though the club also has a need at first base.