The Mariners right-hander was part of a trade on Sunday that sent him to the White Sox.
The Yankees continue to eyeball pitchers from around the league, Steinbrenner told the newspaper, though he wouldn't say which pitchers are in his team's sights.
"We've got our eyes on a bunch of people," he told the Times.
While Steinbrenner has long admired Arizona ace Randy Johnson, the Yankees have had little luck luring the 40-year-old to New York. The Yankees have tried to entice Johnson, but the Diamondbacks haven't been amenable to trade talks about their star starter.
Yankees general manager Brian Cashman doesn't necessarily think pitcher shopping right now is the best move. While the Mariners still have Jamie Moyer and the Pirates' Kris Benson and Atlanta's Russ Ortiz have had their names come up in trade talks, Cashman is looking for his staff to step up this season, especially Kevin Brown, Jon Lieber and Josť Contreras, who was recently reunited with his wife and children -- and may pitch better as a result.
Right now, Cashman seems to be counseling patience.
"We might not be better off making a move for one of the guys out there," Cashman said. "I'm not saying we can't be better. There's a difference between needing to make a move and finding a better option than you have."