Drew, 29, held a mutual option worth $10 million, a hefty price tag for the A's, who can still re-sign the free-agent shortstop should the two sides work out a new deal.
Oakland is very much interested in continuing conversations with Drew to bring him back, according to sources, but should Scott Boras' client go elsewhere, the A's -- who traded shortstop Cliff Pennington to the D-backs just last week -- would be left to explore other options in a lackluster shortstop market that doesn't feature many impact infielders.
Drew, an above-average defender, hit .250 with five home runs and 16 RBIs in 39 games with the A's, following his trade from Arizona on Aug. 20.
Balfour, meanwhile, will collect $4.5 million from the A's in 2013, following an exceptional campaign that resulted in a team-high 75 appearances. The 34-year-old collected 24 saves while posting a 2.53 ERA.
Moving forward, the A's top priority is presumably still Drew, and they must also decide whether to re-sign free agents Jonny Gomes and Brandon McCarthy.
Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.