"The Nationals are not out of it by any means," the source said.
Reports have surfaced that Washington may end up being the only team to offer Lee a seven-year deal, but a source said the Nationals are not offering Lee such a contract and would not get involved in a bidding war with opposing teams like they did with first baseman Mark Teixeira during the 2008 offseason.
Rizzo reiterated on Tuesday afternoon that it is unlikely the Nationals will acquire Lee.
"We have had dialogue with the representative," Rizzo said. "I still don't think we are a real shot to acquire him."
That year, Washington offered Teixeira the most money, but the now-Yankees first baseman told the Nats that they were not ready to win.
Lee may feel differently. The Washington Post reported Tuesday that Lee and Werth are best buddies, and the source confirmed that is the case. They were teammates together in Philadelphia in 2009.
Rizzo believes he can get a top-of-the-rotation pitcher via free agency or a trade. Rizzo said that he could trade some of his prospects for a front-line starter.
The Nationals thought they had an ace in right-hander Stephen Strasburg, but he is out for most of next season after having Tommy John surgery on his right elbow in September.
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.