Buehrle is a Type B free agent, which means the White Sox would get compensation in the form of selection between the first and second round of the June draft if the left-hander was to sign with another team.
Buehrle, who went 13-9 with a 3.59 ERA last season, has pitched at least 200 innings in every season since 2001.
Pierre is also a Type B free agent, but offering him arbitration would have left the White Sox open to re-signing him for next season. Pierre could have ended up with a one-year deal from the White Sox with no more than a 20 percent reduction on his $8.5 million salary in 2010 ($6.8 million).
Pierre hit .279 last season with two home runs.
The White Sox remain free to negotiate with and sign any of their remaining free agents, regardless of whether arbitration was offered.
Buehrle is not expected to accept arbitration from the White Sox, as he is widely expected to receive multiyear offers in free agency.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000.