The source said the two parties are not far apart on getting a deal done.
It was revealed on New Year's Eve that the Nationals have offered LaRoche a two-year deal. Terms of the offer were not disclosed.
LaRoche and Nationals general manager Mike Rizzo could not be reached for comment.
The Nationals have been looking for a first baseman since they allowed slugger Adam Dunn to become a free agent. LaRoche, 31, brings consistency with the bat and glove. He is coming off the best season of his career, hitting .261 with 25 home runs and 100 RBIs for the D-backs. He is also an above-average defensive first baseman. This offseason, the Nationals have put an emphasis on defense, which has been below average the last three years.
If LaRoche signs with the Nationals, he will be reunited with center fielder Nyjer Morgan and reliever Sean Burnett. They were teammates for two-plus seasons from 2007-09 in the Pirates' organization.
In early December, LaRoche told MLB.com that he had interest in playing for the Nationals.
"If we come on the same page, I would definitely have interest in playing for them," LaRoche said.
LaRoche said he believes the Nationals are going in the right direction after signing outfielder Jayson Werth to a seven-year, $126 million contract.
"I think it shows how serious the Nationals are about getting the organization back on track and become a contender in the National League East," LaRoche said. "They are probably tired of watching other teams [spend money and winning]. With the ballpark [Nationals Park] and a little money to spend, they are looking to start over."
LaRoche has played in the big leagues for seven seasons. He is best known for playing with the Braves, but he has also spent time with the Red Sox. During those seven years, LaRoche is a .271 career hitter, with 161 home runs and 569 RBIs.
LaRoche comes from a baseball family. His father, Dave, was a solid relief pitcher for the Angels, Yankees and Indians in the 1970s and '80s, while his brother, Andy, played third base for the Pirates the last three years before becoming a free agent.
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. This story was not subject to the approval of Major League Baseball or its clubs.