The former Red Sox closer has until Thursday to decide whether to accept Boston's offer of salary arbitration. The Red Sox previously had declined a team option on Foulke worth $7.5 million, and the veteran declined to exercise a player option, which would have been worth $3.75 million with a $1.5 million buyout.
Foulke, who has battled injuries the past two seasons after saving 32 games for the World Series champions in 2004, lives in the Phoenix area and has been working out there with a personal trainer.
"Keith has told me that he's healthier now than he was before the 2004 season," Horwits said.
It's unknown just how interested Arizona is in Foulke, but the two sides are expected to continue talks and Foulke might even pay a visit to Chase Field similar to what free agent Mark Mulder did last week.
The D-backs don't seem to be as interested in relievers as they are starters, believing that they have a closer in Jose Valverde and a pair of backups in Jorge Julio and Tony Pena.
"Sometimes closers come from strange places, so I think one way or another we'll have a very good closer," Byrnes said.
After acquiring Doug Davis from the Brewers recently, the D-backs like the way the front end of their rotation shapes up even as they continue to look at ways to get better.
"We can go play today with what we have," Byrnes said. "But we do want to try and get better, and we think we have some ideas to get better. It's just a matter of whether they work or come to fruition this week. We're still pursuing what we can pursue. Until we're told no on a trade or free-agent pursuit, we'll keep trying."
A trade seems to be the most likely route to accomplish that goal. One possibility that sources said has at least been discussed internally would be dealing third baseman Chad Tracy to the Angels for one of their surplus pitchers.
The trade would seem to make sense in that the Angels are looking for help at third base.
A source said the two teams hadn't formally discussed it at the Winter Meetings, but that could change. Of particular interest to the D-backs is lefty Joe Saunders. The 25-year-old burst on the scene last year and went 7-3 with a 4.71 ERA in 13 starts.
Tracy had a bit of a down year in 2006 when he hit .281 with 20 homers and 80 RBIs. Not bad numbers, but they came on the heels of a 2005 season in which he hit .308 with 27 homers and 72 RBIs and raised the expectations the team had of him.
If they did deal Tracy, the D-backs could use highly regarded prospect Alberto Callaspo at third or look to acquire one.
The D-backs met with the Rangers on Sunday night, with Texas interested in right-handers Dustin Nippert and Micah Owings, among others.
Meanwhile, Gregg Clifton, the agent for Mulder, was still trying to get the left-hander's medical records to the D-backs.