Balfour, 34, went 3-2 with a 2.53 ERA in 75 relief appearances for Oakland in 2012. He signed a two-year, $8.1 million contract with the A's before the 2011 season - his deal includes a $4.5 million club option for 2013 with a $350,000 buyout.
Meanwhile, Jane Lee of MLB.com says the A's would like to bring OF Jonny Gomes back next season, although A's manager Bob Melvin said Gomes' situation is a "work in progress."
Gomes, 31, signed a one-year, $1 million contract with the A's this past January. He hit .262 with 18 home runs and 47 RBI in 279 at-bats over 99 games with Oakland in 2012.