Washington was thought to be the front-runners in acquiring Webb's services because of his previous relationship with general manager Mike Rizzo and Phil Rizzo, the senior adviser to the GM. All three worked together with the D-backs as recently as 2006.
However, the source believes the Nationals are concentrating more on acquiring a first baseman to replace Adam Dunn, who signed with the White Sox earlier this month.
MLB.com learned last week that Derrek Lee remains Washington's top target to play the position. Mike Rizzo did not return phone messages left by MLB.com.
The Nationals also remain interested in right-hander Carl Pavano, according to another source, with Washington and the Pavano camp having talks on Sunday.
Washington has not made it a secret that it is looking for starting pitching. Pavano could help the team at the top of the rotation. He's coming off his best season, going 17-11 with a 3.75 ERA with the Twins.
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.