9:26pm: The Phillies have also had talks with Jonathan Papelbon and seem determined to sign him or Madson, according to Jon Heyman of SI.com (on Twitter).
8:18pm: Talks are "advancing, but not complete," a source told ESPN.com's Jerry Crasnick (Twitter links). Agent Scott Boras told Crasnick that the sides are still exchanging proposals.
7:23pm: The Phillies are making a "strong push" to re-sign Ryan Madson, according to ESPN.com's Jayson Stark (on Twitter). Ken Rosenthal of FOX Sports also hears that the Phillies are working hard to complete a deal for Madson. However, GM Ruben Amaro Jr. hasn't ruled other free agents out.
"It's no secret I need a closer," Amaro told Rosenthal. "I am talking to everyone."
Madson, 31, became Philadelphia's full-time closer in 2011, converting 32 saves. He posted a 2.37 ERA with 9.2 K/9, 2.4 BB/9 and a 48.8% ground ball rate in 60 2/3 innings of relief. He's a Type A free agent, but the Phillies won't have to surrender a draft pick to sign their own player. However, they would obtain two picks if the right-hander signs elsewhere after turning down arbitration from Philadelphia.
ESPN.com's Buster Olney reported earlier today that the Blue Jays are taking a "very aggressive" approach in their search for a closer (Twitter link). Though it's not clear if they're targeting Madson, Olney won't be surprised if Toronto ends up with one of the top free agent relievers.