The source said LaRoche's top priority is to re-sign with the Nats, but the slugger is also thinking about his family, which includes two children.
LaRoche already turned down the Nationals' qualifying offer of $13.3 million, and he wants at least a three-year deal. LaRoche has talked to several teams, but the source declined to name them. It has been reported that the Red Sox have interest in LaRoche.
LaRoche is coming off the best season of his career, hitting .271 with 33 home runs and 100 RBIs. He finished seventh in the National League Most Valuable Player voting and won NL Gold Glove and Silver Slugger Awards.
Recently, general manager Mike Rizzo said he wanted LaRoche back in Washington, but expected the first baseman to test to free-agent market.
"We've been in contact [with his representative]," Rizzo said. "We've touched base a couple times since the season ended. We continue to talk and we'll see where it leads us."
If the Nationals are unable to re-sign LaRoche, they could put Michael Morse or Tyler Moore back at first base. Morse's best season of his Major League career came while playing first. In 2011, Morse was Washington's MVP, hitting .303 with 31 home runs and 95 RBIs.
Moore spent most of his time in left field in 2012, but he's a first baseman by trade. As a first baseman, Moore hit a combined 62 home runs for Class A Potomac and Double-A Harrisburg.
Bill Ladson is a reporter for MLB.com and writes an MLBlog, All Nats All the time. He also could be found on Twitter @WashingNats. MLB.com reporter Paul Hagen contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.