Gordon, 32, was 5-0 with an International League-leading 1.14 ERA for Triple-A Lehigh Valley in the Philadelphia Phillies' organization.
A Yankees spokesman said that Gordon has an opt-out in his contract that can be exercised on Wednesday, at which time the team would discuss his situation in more detail.
Gordon stated that he has already signed with the Yankees after leaving Coca-Cola Park in Allentown, Pa., and added that he has been told to get ready for a possible start on Thursday.
In an interview with YESNetwork.com, Gordon said, "I'm really looking forward to helping the Yankees. ... I don't know if [the start is] 100 percent. I was told be mentally prepared to start on Thursday. That could change."
A converted outfielder, Gordon's only previous big league experience came in 2008 with the Rangers, when he pitched four innings.
The Yankees have been tossing around the names of long reliever Hector Noesi, plus Minor Leaguers David Phelps and Adam Warren, as other choices to take Bartolo Colon's rotation slot on Thursday.
Manager Joe Girardi acknowledged that he knew of Gordon but would not discuss the move in any detail.
"He is not our property yet, so I have not been told that he is a New York Yankee," Girardi said. "But we'll see."