All three players have been linked to some extent with the Yankees this offseason, and New York is quite familiar with what Damon and Matsui are capable of contributing after they starred on the 2009 World Series-winning club.
But Girardi said that their history in pinstripes wouldn't necessarily give them an edge over Ibanez. The 39-year-old free agent hit .245 with 20 home runs and 84 RBIs in 144 games for the Phillies last year.
While Ibanez struggled against left-handed pitching in 2011, posting a .211 average in 133 at-bats, the Yankees already have Andruw Jones on the roster to face southpaws.
"When you think about Raul Ibanez, he has had success wherever he has [gone]," Girardi said. "There could be other things that could happen; I can't tell you it is going to be one of those three guys, or anyone. But obviously, we know they know how to play here."
Girardi said that it would be preferable to import a left-handed bat, considering Yankee Stadium's dimensions.
"It doesn't have to be, but it does make some sense," Girardi said.
It has been reported that the Yankees have only about $2 million remaining in their budget to pursue a DH, though as managing general partner Hal Steinbrenner's willingness to spend $10 million on right-hander Hiroki Kuroda exhibited, there is some flexibility in those figures.
Damon was disappointed when the Rays signed free-agent slugger Luke Scott, effectively ending his one-year stint with the club, and is thought to be very open to returning to New York. Matsui, who loved his time with the Yankees, is looking for his next uniform after spending one season with the A's.
"Obviously, we know what Johnny and Matty have meant to this organization over the years, and how they've been successful in New York," Girardi said. "I'm curious to see how it is all going to shake out."
Girardi said that the possibility of adding another DH has kept him from playing with too many lineup combinations on paper, though he mentioned that the Yankees will "definitely" look at second baseman Robinson Cano in the No. 3 spot during Spring Training.
The skipper also said that he had no problem with Mark Teixeira's intention to try bunting for singles against tough defensive shifts now and again, noting that it is a topic they have talked about in the past.
"He'll have to pick his spots, but he's a talented guy," Girardi said of Teixeira. "A lot of times when they're that far over, it doesn't have to be a perfect bunt. It's not like they're going to play him like [Brett Gardner]."
Girardi's appearance was to join Modell's CEO Mitchell Modell in helping offer support to the Children's Alopecia Project, devoted specifically to children living with the incurable autoimmune hair loss disease.
One thousand New York Giants NFC championship hats were donated at the event, with Girardi signing autographs for children as he encouraged them to have confidence in themselves.
"Just because you don't have hair doesn't change who you are," Girardi said. "I think it's important that a lot of times when people go through things, they're not feeling like they're the only ones."