In an email, Werth dismissed the notion that he was actively “recruiting” Madson to join the Nationals. But Werth did reveal that he has spoken to Madson about the state of the Nationals’ franchise.

“I heard I was recruiting him,” Werth said in the email. “I laughed. Did have a conversation about the Nats and the direction of the ball club, but I’m sure Ryan will make a sound decision for him and his family in due time. I haven’t heard anything, but who wouldn’t wanna have Doggie on their team?”

(“Doggie” is a variation on Mad Dog, Madson’s nickname.)

Madson and the Phillies, according to several reports, came close to finalizing a contract for $44 million over four years Tuesday night. But the sides did not close the deal, and this evening Ken Rosenthal of FoxSports.com reported the Nationals could enter the race for Madson. General Manager Mike Rizzo did not immediately return a message.

Madson would give the Nationals a devastating back end to a bullpen that already includes Drew Storen, Tyler Clippard and Henry Rodriguez. Acquiring Madson would also enable the Nationals to consider trading Storen, Clippard or Rodriguez in order to land the center fielder they covet.

Madson, 31, has been a valuable and consistent reliever for the Phillies. As they have won the past five straight National League East titles, Madson has pitched at least 53 relief innings every season. Madson took over the closer’s role full time this season and saved 32 games in 34 chances with a 2.37 ERA over 60 2/3 innings.

(His worst moment this year came against the Nationals, when Ryan Zimmerman hit a walk-off grand slam to cap a six-run ninth inning against him in August.)

While Madson would provide an experienced closer, he would also come at a significant cost. The reported terms of his near-deal with the Phillies would have made Madson one of the most well-paid closers of all-time. Madson is also a Type A free agent, which means the Nationals would lose their first-round pick (No. 16 overall) to the Phillies in 2012 as compensation. Also, Storen and Rodriguez make minimal salaries and Clippard is eligible for arbitration for the first time.

Werth left the Phillies in free agency last winter by signing a seven-year, $126 million contract with the Nationals. Like Werth, Madson is represented by Scott Boras, the same high-profile agent who represents Stephen Strasburg, Bryce Harper and several other Nationals players.