But it wasn't until Sunday morning, sitting in the visitors' dugout, that he realized it would be his last time here.
"I didn't think about that," Geren said. "I always enjoy coming here, because it reminds me a lot of when I was younger."
A catcher during his playing days, Geren made his Major League debut with the Yankees. He spent four seasons with the Bombers, from 1988-91, and built up plenty of memories of the ballpark that was his home field.
And though Geren doesn't keep much in the way of souvenirs from his time on the diamond, there are a few special items from Yankee Stadium that he's been holding onto for years.
"I don't save a lot of memorabilia, really, but what I do [have] is from here," he said. "I'm not a big collector, but I've got pictures in that dugout with my son when he was 1, pictures with Joe DiMaggio in the dugout, Mickey Mantle.
"I always moved around so much as a Minor Leaguer every year, so I couldn't really collect anything. Because I was moving all the time, I just never really got into it. But those are two things that I have."
During his pregame media session, he turned the tables when he began addressing questions to a group of reporters.
He wanted to know what would happen to the current stadium and what the new ballpark would be like. He listened closely as he was told that the new stadium would be larger in size but smaller in capacity.
"Actually, it's nice, because as many memories as I have in this stadium, I'm looking forward to seeing something like that," he said.
The A's dropped the first two games of their three-game series against the Yankees. And though Geren took some time to reminisce about his career with New York before the finale, when he steps off the Yankee Stadium field for the last time on Sunday afternoon, he wants it to come with an Oakland win.
Samantha Newman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.