"We understand he doesn't have the same fastball that he used to have," Giants general manager Bobby Evans said, adding that limited roster flexibility increases the difficulty of promoting Nathan to the Majors in September.
"At the same time, he can at least get a chance to get looked at and we'll see where things fall," Evans said. "I didn't put any promises out there."
Giants manager Bruce Bochy welcomed the possibility of bringing aboard Nathan, who has 377 saves in 16 big league seasons.
Said Bochy, "He brings you an experienced veteran who's been in the fire. He's not going to be afraid. You know that about him."
Nathan went to the Minnesota Twins with left-hander Francisco Liriano and right-hander Boof Bonser in an ill-fated trade on Nov. 14, 2003, that brought catcher A.J. Pierzynski to the Giants. Pierzynski alienated numerous teammates while lasting just one season in San Francisco. By contrast, Liriano developed into an All-Star and Nathan recorded 35 or more saves nine times in 10 seasons.
Nathan, 41, made three appearances for the Cubs last month, including a pair of shutout innings, before they designated him for assignment Aug. 5.
Evans said he and Nathan discussed the potential for a deal during last year's Winter Meetings. But Nathan's desire for a Major League contract dissuaded the Giants from signing him.
"It just didn't fit for us at that moment," Evans said.
Nathan, a converted shortstop, began his professional career with the Giants as a sixth-round Draft selection in 1995.
• Bochy said reliever Cory Gearrin (right shoulder) will attempt to accelerate his recovery by pitching Wednesday for Triple-A Sacramento. ... Outfielder Mac Williamson (left shoulder) is on day-to-day playing status with Sacramento. ... Left-hander Josh Osich (forearm) allowed a run in a one-inning injury rehabilitation outing for Sacramento on Monday. Bochy said Osich will try throwing on back-to-back days Thursday and Friday.
Chris Haft has covered the Giants since 2005, and for MLB.com since 2007. Follow him on Twitter at @sfgiantsbeat and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.