Towers said he had interest in veterans David Eckstein and Omar Vizquel, in addition to a few names he didn't want to divulge.
"There are a couple of other guys, too," Towers said. "We've got three or four options."
Currently, the Padres have Luis Rodriguez -- who filled in admirably for Greene during the final two months of the season after Greene broke his left hand.
But Rodriguez -- who hit .315 in August and .304 in September -- and Edgar Gonzalez, who also saw time at shortstop last season, are second basemen by trade. By adding a veteran shortstop, the Padres could slide Rodriguez back to his natural position.
Eckstein, who turns 34 on Jan. 20, can play second base or shortstop, and he hit .265 last season with the Blue Jays and D-backs.
Vizquel will be 42 in April. He hit .222 last season with the Giants, but still showed the kind of defense that made him an 11-time Gold Glove Award winner.
Mark Grudzielanek might be another possibility, though he's played only eight games at shortstop since 2000. Luis Rivas and Alex Cintron are available, though it's not known if the Padres have interest in the two free agents.
Other than shortstop, Towers said he would still like to add a backup catcher -- Towers has had talks with veteran Brad Ausmus, who lives in nearby Del Mar -- as well as depth in the starting rotation, even after signing Kevin Correia last month.
"I think we need at least one starting piece," Towers said. "Like Correia, most of our stuff is going to be late. We're hoping there's still going to be inventory there."
The rotation currently includes Jake Peavy, Chris Young and Cha Seung Baek, though Correia figures to earn a spot. Rookies Josh Geer and Wade LeBlanc also figure to be in the mix during Spring Training, which begins Feb. 14, when pitchers and catchers report.