"We're close," Gordon's agent Rick Thurman said on Friday. "We don't have a deal yet, but we're close."
Gordon, 41, was 5-4 with a 5.16 ERA in 34 games for the Phillies last season. The right-hander last appeared in a game on July 5 before being shut down and having a procedure called ulnar-nerve decompression.
Over his 20 big league seasons, Gordon has a 3.94 ERA with 158 saves.
Gordon would help bolster a bullpen that has lost Brandon Lyon and Juan Cruz to free agency.
Chad Qualls will enter Spring Training as the team's closer, with Tony Pena and Jon Rauch as the setup men along with lefty Scott Schoeneweis.
"I think to be the kind of team we need to be I think we need to be better offensively," GM Josh Byrnes said when asked after the signing of Jon Garland on Thursday what other area of the team he would like to improve before Spring Training.
"But I think we feel a lot of that improvement can come just from continuing to devote playing time to very talented young players. As far as changing anything, there's a chance we could make a tweak in the bullpen, but there's a chance we don't."
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.