One possibility is Stephen Drew. Drew was dealt to the A's from the Diamondbacks, and had a decent finish to the season. Drew posted an OBP of .326, but the Athletics declined to pick up his $10 million option and let him off on the free agent market.
The A's have the possibility of Japanese infielder Hiroyuki Nakajima, who had the chance to sign with the New York Yankees but declined the opportunity.
The A's could also be potentially looking at Yunel Escobar of the Marlins. Beane has reportedly met with the Marlins to talk about the shortstop. Escobar has good defensive skill and posted an OBP around .353, although he does have a bit of a black PR mark for a homophobic slur.