General manager Ed Wade spoke with Peter Greenberg, Garcia's agent, on Thursday, but Wade said that he is not at the point where he's ready to make an offer.
"[Greenberg] was making calls to the teams that he knew showed up to the workout," Wade said. "It's an ongoing feeling-out process. We're not at the point to make an offer. We asked them to provide medical information, which they did. [Team medical director] Dr. [David] Lintner will review it, and we'll go from there."
Garcia, a former Houston farmhand who was traded to Seattle as part of the Randy Johnson trade 10 years ago, had season-ending shoulder surgery early in 2007. He has spent the better part of a year rehabbing, and he has drawn a great deal of interest from clubs looking for pitching help in the final stages of the regular season.
Garcia, 33, has a career record of 117-76 with a 4.07 ERA over nine seasons with the Mariners, White Sox and Phillies.
Alyson Footer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.