NEW YORK (AP) -- The competition to buy a small coffee chain is getting steamy, with Starbucks (SBUX 1.09%) and actor Patrick Dempsey among those vying to become its new owners.

Starbucks confirmed that it is participating in a bankruptcy auction Thursday to buy Tully's Coffee, which has 47 company-owned locations in Washington and California. Tully's filed for Chapter 11 bankruptcy protection in October.

Dempsey, who gained the nickname "McDreamy" on the TV show "Grey's Anatomy" set in a fictional Seattle hospital, also said last week that he wants to rescue the chain. Also in the running is Baristas Coffee (BCCI 2.86%), which operates a chain of drive-thru espresso stands featuring female employees in skimpy outfits.

A representative for Starbucks declined to provide details of the company's bid, citing the court's confidentiality orders. But last week, the Seattle Times reported that Starbucks only wants to buy about half of Tully's chains. Both chains are based in Seattle.

The auction process is not public. The outcome is expected to be filed in court Friday.